1
The class mark of 0-10 is —
💡 Hint:
The average.
Explanation:
5.
Class 10 · Maths · Chapter 13 · बिहार बोर्ड (BSEB)CBSE · NCERT 2026-27
Statistics
Statistics
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1. Read — Direct mean · assumed mean · step deviation · mode · median, diagram, worked example, board tip
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4. The memory figure shows the same mean 18 from three methods and a strip for the modal class.
In NCERT 2026-27 this is Chapter 13; in Bihar’s older book Statistics is Chapter 14. Progress stays in this browser.
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- 1 Direct mean and the class mark
- 2 Assumed mean
- 3 Step deviation
- 4 The modal class
- 5 Cumulative frequency and the median
- 6 Continuous classes and the empirical relation
- 7 Comparing the three
- Chapter winner — every lesson at mastery ★
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📄 PDF download — notes + answer key
Direct mean and the class mark
प्रत्यक्ष माध्य और वर्ग चिह्न · NCERT 13.2 · preparing Exercise 13.1
One representative for each classNotes
A grouped table does not list every student separately. The representative of a class is the class mark.
x̄ = Σfixi / Σfi. xi = (lower limit + upper limit)/2. The frequency fi is the count of that class. Exercise 13.1 is these means.
Three columns are enoughActivity
xi, fi and fixi. Below them, Σfi and Σfixi. Divide. Keep the unit of the data: marks, rupees, centimetres. Do not write a class limit in place of the class mark.
Worked exampleExample
Question: Class marks 5, 15, 25 and frequencies 2, 3, 5. Find the mean.
Formula: x̄ = Σfixi / Σfi.
Substitution: fixi = 10, 45, 125. Σfixi = 180. Σfi = 10. 180/10 = 18.
Answer: The mean is 18.
10-second revision
- Class mark = average of the limits
- Mean = 180/10 = 18
- 13.1 is the mean exercise
Board tip · BSEBBoard tip
In a BSEB answer write Σfixi and Σfi on two separate lines.
Board tip · CBSEBoard tip
On CBSE do not write 0 or 10 as the mark of the class 0-10. It is 5.
Check your understandingall correct = mastery ★
2
The direct mean is Σfi / Σfixi.
Explanation:
False — it is the other way, Σfixi / Σfi.
3
When the sum of fixi is 180 and the sum of fi is 10, the mean is ______.
💡 Hint:
180/10.
Explanation:
18.
4
Exercise 13.1 asks for —
💡 Hint:
The first exercise.
Explanation:
The mean.
5
The class mark is the frequency.
Explanation:
False — the frequency is fi.
6
Write the class marks of 10-20 and 20-30.
Model answer (board format)
15 and 25.
Check your answer:
Assumed mean
कल्पित माध्य · NCERT 13.2 · di = xi − a
Choose the middle markNotes
For large numbers, put the deviation in place of xi. a may be any class mark. The middle one is usually easy.
x̄ = a + Σfidi / Σfi, and di = xi − a. If a = 15, di = −10, 0, 10 and fi = 2, 3, 5, then Σfidi = 30 and the mean is 18 again.
Do not drop a minus signActivity
An xi smaller than a gives a negative di. fidi may be negative too. In the sum, negatives are added, not ignored. If Σfidi is zero, the mean is exactly a.
Worked exampleExample
Question: a = 15, the sum of fidi is 30, Σfi = 10. Find the mean.
Formula: x̄ = a + Σfidi / Σfi.
Substitution: 15 + 30/10 = 15 + 3 = 18.
Answer: 18.
10-second revision
- di = xi − a
- 15 + 3 = 18
- A negative deviation stays in the sum
Board tip · BSEBBoard tip
In a BSEB answer keep the line for a and the line for di apart.
Board tip · CBSEBoard tip
On CBSE do not treat the assumed mean as the final answer. Σfidi/Σfi is added to it.
Check your understandingall correct = mastery ★
1
If a = 15 and Σfidi/Σfi = 3, the mean is —
💡 Hint:
Add it to a.
Explanation:
18.
2
di = a − xi.
Explanation:
False — di = xi − a.
3
If xi = 5 and a = 15, then di = ______.
💡 Hint:
5 − 15.
Explanation:
−10.
4
a = 25, Σfidi = −20, Σfi = 10. Find the mean.
Model answer (board format)
25 + (−20)/10 = 25 − 2 = 23.
Check your answer:
Step deviation
पग-विचलन · NCERT 13.2 · ui = (xi − a)/h
A common factor comes outsideNotes
When every di is divisible by the same h, write ui = di/h. It is easier when h is the class width.
x̄ = a + (Σfiui / Σfi) × h. If a = 15, h = 10, ui = −1, 0, 1 and fi = 2, 3, 5, then Σfiui = 3 and the mean is 15 + 3 = 18. The three methods give one answer.
Bring h back at the endActivity
You divided by h to make ui. The formula multiplies by h again. Forget that product and the answer is too small by a factor h. The book says a and h may be any non-zero numbers, as long as ui = (xi − a)/h.
Worked exampleExample
Question: a = 15, h = 10, Σfiui = 3, Σfi = 10. Find the mean.
Formula: x̄ = a + (Σfiui / Σfi) × h.
Substitution: 15 + (3/10) × 10 = 15 + 3 = 18.
Answer: 18.
10-second revision
- ui = (xi − a)/h
- Multiply by h at the end
- The answer is 18 again
Board tip · BSEBBoard tip
In a BSEB answer show both the ui column and the fiui column.
Board tip · CBSEBoard tip
On CBSE do not write (Σfiui/Σfi) itself as the mean. a and h are still there.
Check your understandingall correct = mastery ★
1
If a = 15, h = 10 and Σfiui/Σfi = 0.3, the mean is —
💡 Hint:
0.3 × 10 = 3.
Explanation:
18.
2
The step-deviation mean is a different number from the direct mean.
Explanation:
False — the book says all three agree.
3
If di = −10 and h = 10, then ui = ______.
💡 Hint:
Divide.
Explanation:
−1.
4
h appears at the end because —
💡 Hint:
Bring the step back.
Explanation:
h had already been cancelled in ui.
5
a = 20, h = 5, Σfiui = 8, Σfi = 4. Find the mean.
Model answer (board format)
20 + (8/4)×5 = 20 + 2×5 = 30.
Check your answer:
The modal class
बहुलक वर्ग · NCERT 13.3 · Exercise 13.2
The class with the tallest frequencyNotes
In ungrouped data the mode is the value that appears most often. In grouped data we only identify the modal class, and then the formula gives a value inside it.
Mode = l + ((f1 − f0)/(2f1 − f0 − f2)) × h. Exercise 13.2 is this. If there is more than one mode, the book does not take that table.
f0 and f2 are the neighboursActivity
f1 belongs to the modal class. f0 is the one before it, f2 the one after it. If the first class is modal, f0 = 0. If the last is modal, f2 = 0. l is the lower limit, not the upper one.
Worked exampleExample
Question: Frequencies 4, 8, 15, 6 and equal width 10. The modal class is 20-30. Find the mode.
Formula: l + ((f1 − f0)/(2f1 − f0 − f2)) × h.
Substitution: l = 20, f1 = 15, f0 = 8, f2 = 6, h = 10. 20 + (7/(30 − 8 − 6)) × 10 = 20 + (7/16) × 10 = 24.375.
Answer: 24.375.
10-second revision
- f1 is the greatest frequency
- The mode is 24.375
- 13.2 is the mode exercise
Board tip · BSEBBoard tip
In a BSEB answer write the three numbers f0, f1 and f2 before the formula.
Board tip · CBSEBoard tip
On CBSE do not make the upper limit of the modal class into l.
Check your understandingall correct = mastery ★
1
For frequencies 4, 8, 15, 6 the mode is —
💡 Hint:
(7/16)×10.
Explanation:
24.375.
2
The modal class has the smallest frequency.
Explanation:
False — the greatest.
3
If the first class is modal, f0 = ______.
💡 Hint:
There is no class before it.
Explanation:
0.
4
The subject of Exercise 13.2 is —
💡 Hint:
The exercise after section 13.3.
Explanation:
Mode.
5
l is the lower limit of the modal class.
Explanation:
True.
6
l = 10, h = 5, f1 = 12, f0 = 8, f2 = 4. Find the mode.
Model answer (board format)
10 + ((12−8)/(24−8−4))×5 = 10 + (4/12)×5 = 10 + 5/3 = 35/3.
Check your answer:
Cumulative frequency and the median
संचयी बारंबारता और माध्यक · NCERT 13.4 · Exercise 13.3
The class of n/2Notes
Cumulative frequency is made by adding this class frequency to the previous total. n is the total frequency.
Median = l + ((n/2 − cf)/f) × h. Exercise 13.3 is this. For frequencies 5, 8, 4, 3 and width 10, starting at 0-10, n/2 = 10, the median class is 10-20 and the median is 16.25.
cf belongs to the previous classActivity
If the median class is 10-20 and the first cumulative frequency is 5, then cf = 5, f = 8 and l = 10. Do not fold the 8 into cf. Whether n is even or odd, the grouped formula always uses n/2.
Worked exampleExample
Question: n = 20, median class 10-20, cf = 5, f = 8, h = 10. Find the median.
Formula: l + ((n/2 − cf)/f) × h.
Substitution: 10 + ((10 − 5)/8) × 10 = 10 + 6.25 = 16.25.
Answer: 16.25.
10-second revision
- n/2 chooses the class
- cf goes up to the previous class
- The median in the example is 16.25
Board tip · BSEBBoard tip
In a BSEB answer show the cumulative column for the whole table, then choose the class.
Board tip · CBSEBoard tip
On CBSE, if n/2 − cf comes out negative, the class is wrong. Take the other class.
Check your understandingall correct = mastery ★
1
For n = 20, cf = 5, f = 8, l = 10, h = 10 the median is —
💡 Hint:
10 + 6.25.
Explanation:
16.25.
2
The grouped median uses (n+1)/2.
Explanation:
False — the formula uses n/2.
3
The subject of Exercise 13.3 is ______.
💡 Hint:
Cumulative frequency.
Explanation:
The median.
4
Frequencies are 5, 8, 4, 3. Write n and n/2. Which is the median class if the classes are 0-10, 10-20, 20-30, 30-40?
Model answer (board format)
n = 20, n/2 = 10. Cumulative 5, 13. 5 < 10 and 13 ≥ 10, so the median class is 10-20.
Check your answer:
Continuous classes and the empirical relation
सतत वर्ग और आनुभविक संबंध · Note to the reader · 3 median = mode + 2 mean
Join the limits firstNotes
Classes such as 1-4 and 5-8 have a gap. Before the mode or the median, subtract and add half the gap. If the gap is 1, half is 0.5. The classes become 0.5-4.5 and 4.5-8.5.
3 median = mode + 2 mean is empirical, and it does not fit every table exactly. An ogive also needs continuous classes. That is a note. Exercises 13.1 to 13.3 do not ask you to draw an ogive.
Half the gap on both sidesActivity
The gap between 5 and 4 is 1. The lower limit becomes 1 − 0.5 = 0.5 and the upper 4 + 0.5 = 4.5. The next class starts at 5 − 0.5 = 4.5, so the limits meet. The width stays 4.
Worked exampleExample
Question: Make the classes 1-4 and 5-8 continuous. Write the width.
Formula: Half the gap = (5 − 4)/2 = 0.5.
Substitution: 1 − 0.5 = 0.5, 4 + 0.5 = 4.5, 5 − 0.5 = 4.5, 8 + 0.5 = 8.5.
Answer: 0.5-4.5 and 4.5-8.5. The width is 4.
10-second revision
- Half the gap on both limits
- The width does not change
- The empirical relation is not proved every time
Board tip · BSEBBoard tip
In a BSEB answer write one line of making the classes continuous before the formula.
Board tip · CBSEBoard tip
On CBSE do not write 3 median = mode + 2 mean as a check that every table must pass.
Check your understandingall correct = mastery ★
1
The continuous forms of 1-4 and 5-8 are —
💡 Hint:
Half the gap is 0.5.
Explanation:
0.5-4.5 and 4.5-8.5.
2
Making them continuous changes the width from 4 to 5.
Explanation:
False — the width stays 4.
3
In the empirical relation, 3 median = mode + ______ mean.
💡 Hint:
Two means.
Explanation:
2.
4
The 2026-27 exercises, an ogive —
💡 Hint:
The name is in the note.
Explanation:
The exercises do not ask for an ogive.
5
Write the classes 10-19 and 20-29 in continuous form.
Model answer (board format)
The gap is 1, half is 0.5. The classes are 9.5-19.5 and 19.5-29.5.
Check your answer:
Comparing the three
तीनों की तुलना · First question of Exercise 13.3 · summary 13.5
One table, three answersNotes
The first question of Exercise 13.3 asks for the median, the mean and the mode of electricity use, and then a comparison. The three need not be equal.
The summary keeps four points: the three methods for the mean, the mode formula, cumulative frequency, and the median formula. Changing the method does not change the mean. A question with x and y needs both the total-frequency equation and the median equation.
Two equations, two unknownsActivity
If the total n is given, the sum of all frequencies is n. Identify the median class and set the formula equal to the given median. One equation is the sum, the other is the median. Then find x and y.
Worked exampleExample
Question: The mean came out 18 by all three methods. Must the mode also be 18?
Formula: 3 median = mode + 2 mean is only empirical.
Substitution: In the earlier example the mode was 24.375 and the mean was 18. They are not equal.
Answer: No. The mean is one number, and the mode may differ.
10-second revision
- The three means are one number
- Mode and median may differ
- Two equations for x and y
Board tip · BSEBBoard tip
In a BSEB answer write the three numbers together on the last line of a comparison.
Board tip · CBSEBoard tip
On CBSE do not invent a new mean by changing the method. If they differ, check the columns.
Check your understandingall correct = mastery ★
1
If all three methods give the mean 18, the true statement is —
💡 Hint:
The methods are simplifications.
Explanation:
The mean is the same one.
2
The electricity question asks only for the mode.
Explanation:
False — median, mean and mode, all three.
3
The summary has ______ methods for the mean.
💡 Hint:
Direct, assumed, step.
Explanation:
3.
4
A median question with x and y needs equations —
💡 Hint:
Two unknowns.
Explanation:
Two equations.
5
The mean is 20 and the mode is 18. What median does the empirical relation give? Why is this check not fully certain?
Model answer (board format)
3 median = 18 + 40 = 58, so the median is 58/3. This is empirical, and the median from the formula on the table may differ.
Check your answer:
❓ Full question bank — with answers and explanations — 65 questions
Pick a type. The 35 lesson checks are separate — each lesson has as many as its topic needs. All correct earns mastery ★.
BSEB modelpractice · not annual60 tried · 0 correctMultiple choiceMCQ120 tried · 0 correctTrue / falseTrue / false80 tried · 0 correctFill in the blanksFill80 tried · 0 correctMatchMatch20 tried · 0 correctAssertion–reasonAssertion–reason50 tried · 0 correctBalancingBalancing40 tried · 0 correctIdentifyIdentify20 tried · 0 correctShort and longVSA, SA, LA120 tried · 0 correctCBSE-stylenot a PYQ60 tried · 0 correct
No question is marked as a verified past paper. The BSEB set is a model for practice. CBSE items are CBSE-style, not a copy of any year’s paper.
Multiple choice
0/12Pick one option. A wrong try brings a hint.
1
The mark of class 0-10 is —
💡 Hint:
Average.
Explanation:
5.
2
If Σfixi = 180 and Σfi = 10, the mean is —
💡 Hint:
Divide.
Explanation:
18.
3
If a = 15 and Σfidi/Σfi = 3, the mean is —
💡 Hint:
Add.
Explanation:
18.
4
If a = 15, h = 10 and Σfiui/Σfi = 0.3, the mean is —
💡 Hint:
Multiply by h.
Explanation:
18.
5
The mode for frequencies 4, 8, 15, 6 is —
💡 Hint:
(7/16)×10.
Explanation:
24.375.
6
The median for n = 20, cf = 5, f = 8, l = 10, h = 10 is —
💡 Hint:
10 + 6.25.
Explanation:
16.25.
7
The order of 13.1, 13.2, 13.3 is —
💡 Hint:
The book order.
Explanation:
Mean, mode, median.
8
The continuous form of 1-4, when the next starts at 5, is —
💡 Hint:
Half the gap.
Explanation:
0.5-4.5.
9
If xi = 5 and a = 15, di is —
💡 Hint:
xi − a.
Explanation:
−10.
10
If the first class is modal, f0 is —
💡 Hint:
No neighbour.
Explanation:
0.
11
In the empirical relation the factor of the mean is —
💡 Hint:
2 mean.
Explanation:
2.
12
h is at the end of step deviation because —
💡 Hint:
Multiply back.
Explanation:
It was cancelled in ui.
True or false
0/81
The three mean methods give one answer.
Explanation:
True.
2
di = a − xi.
Explanation:
False — xi − a.
3
The modal class has the greatest frequency.
Explanation:
True.
4
The grouped median uses (n+1)/2.
Explanation:
False — n/2.
5
Making classes continuous changes the width.
Explanation:
False — the width stays the same.
6
3 median = mode + 2 mean is an identity for every table.
Explanation:
False — it is empirical.
7
Exercise 13.2 is about the mode.
Explanation:
True.
8
l is the upper limit.
Explanation:
False — the lower limit.
Fill in the blanks
0/81
The mark of 0-10 is ______.
💡 Hint:
5.
Explanation:
Average.
2
180/10 = ______.
💡 Hint:
18.
Explanation:
Direct mean.
3
5 − 15 = ______.
💡 Hint:
−10.
Explanation:
di.
4
One mode example is ______.
💡 Hint:
24.375.
Explanation:
Add (7/16)×10.
5
One median example is ______.
💡 Hint:
16.25.
Explanation:
10 + 6.25.
6
Half the gap, when the gap is 1, is ______.
💡 Hint:
0.5.
Explanation:
1/2.
7
There are ______ methods for the mean.
💡 Hint:
3.
Explanation:
The summary.
8
If n = 20, then n/2 = ______.
💡 Hint:
10.
Explanation:
Half.
Match
0/21
Match the name with the formula.
Column B: A. l + ((n/2−cf)/f)×h · B. Σfixi/Σfi · C. a + Σfidi/Σfi · D. l + ((f1−f0)/(2f1−f0−f2))×h
1. Direct
2. Assumed
3. Mode
4. Median
Explanation:
Direct is a quotient, assumed uses a, mode uses three f values, median uses cf.
2
Match the exercise with the topic.
Column B: A. The continuous-class condition · B. Mean · C. Mode · D. Median
1. 13.1
2. 13.2
3. 13.3
4. Note to the reader
Explanation:
13.1 mean, 13.2 mode, 13.3 median, and the note has continuous classes.
Assertion–reason
0/5Check both statements, then see whether the reason explains the assertion.
1
Assertion (A): All three methods give the mean 18.
Reason (R): Assumed mean and step deviation are simpler forms of the direct method.
Explanation:
Both are true and R explains A.
2
Assertion (A): The grouped median is the (n+1)/2 th value.
Reason (R): The grouped formula uses n/2 and the cumulative frequency.
Explanation:
A puts the ungrouped even-odd rule onto grouped data, so it is false. R is true.
3
Assertion (A): The class with frequency 15 is the modal class when the neighbours are 8 and 6.
Reason (R): Therefore the mode is exactly 15.
Explanation:
A is true. R is false, the mode is 24.375.
4
Assertion (A): 1-4 and 5-8 become 0.5-4.5 and 4.5-8.5 when made continuous.
Reason (R): The three methods for the mean give one answer.
Explanation:
Both are true, but R does not explain the continuous classes.
5
Assertion (A): cf is the cumulative frequency before the median class.
Reason (R): n/2 − cf removes that previous total.
Explanation:
Both are true and R explains A.
Coefficient practice
0/4These chemistry lines are not a result of this maths chapter. They are only practice in filling coefficients. A blank means 1.
1
This is coefficient practice and not a result of this chapter. In the water line, Fill coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
2
This is coefficient practice and not a result of this chapter. In the line of H2 and O2, Fill coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
3
This is coefficient practice and not a result of this chapter. In this coefficient line, Fill coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
4
This is coefficient practice and not a result of this chapter. In the line with blank spaces, Fill coefficients (blank = 1).
H2 + O2 → H2O
Explanation: 2H2 + O2 → 2H2O
Classify
0/21
Place each measure in its family.
Σfixi / Σfi
The class with the greatest fi
The cumulative frequency at n/2
a + (Σfiui/Σfi)×h
Explanation:
Both mean formulas are the mean. The large fi is the mode. n/2 is the median.
2
Place each exercise with its job.
Plants, wages, pocket money
Ages of patients, cars
Electricity and x, y
Mean literacy
Explanation:
13.1 is the mean, 13.2 the mode, 13.3 the median. Literacy is also in 13.1.
Very short answer
0/51
Write the direct-mean formula.
Model answer (board format)
Σfixi / Σfi.
Check your answer:
2
Write the mode formula.
Model answer (board format)
l + ((f1 − f0)/(2f1 − f0 − f2)) × h.
Check your answer:
3
Write the median formula.
Model answer (board format)
l + ((n/2 − cf)/f) × h.
Check your answer:
4
Write the step-deviation formula.
Model answer (board format)
a + (Σfiui / Σfi) × h.
Check your answer:
5
Write the empirical relation.
Model answer (board format)
3 median = mode + 2 mean.
Check your answer:
Short answer
0/41
a = 15, h = 10, Σfiui = 3, Σfi = 10. Find the mean.
Model answer (board format)
15 + (3/10)×10 = 18.
Check your answer:
2
l = 20, f1 = 15, f0 = 8, f2 = 6, h = 10. Find the mode.
Model answer (board format)
20 + (7/16)×10 = 24.375.
Check your answer:
3
n = 20, l = 10, cf = 5, f = 8, h = 10. Find the median.
Model answer (board format)
10 + ((10−5)/8)×10 = 16.25.
Check your answer:
4
Make the classes 10-19 and 20-29 continuous.
Model answer (board format)
9.5-19.5 and 19.5-29.5.
Check your answer:
Long answer
0/31
Marks 5, 15, 25 and frequencies 2, 3, 5. Find both the direct mean and the assumed mean. a = 15.
Model answer (board format)
fixi = 10 + 45 + 125 = 180. Σfi = 10. Direct = 18. di = −10, 0, 10. fidi = −20 + 0 + 50 = 30. Assumed = 15 + 3 = 18.
Check your answer:
2
Frequencies 5, 8, 4, 3 and classes 0-10, 10-20, 20-30, 30-40. Find the median class and the median.
Model answer (board format)
n = 20, n/2 = 10. Cumulative 5, 13, 17, 20. Median class 10-20, cf = 5, f = 8, h = 10. Median = 10 + (5/8)×10 = 16.25.
Check your answer:
3
A student writes the mode as the greatest frequency 15. With l = 20, f0 = 8, f2 = 6 and h = 10, find the correct mode and name the mistake.
Model answer (board format)
15 is the frequency of the modal class, not the mode. 20 + ((15−8)/(30−8−6))×10 = 24.375.
Check your answer:
BSEB model paper · practice
0/6This model set is for practice. It is not a question from any year’s annual examination.
1
If a = 25, Σfidi = −20 and Σfi = 10, the mean is —
💡 Hint:
25 − 2.
Explanation:
23.
2
If l = 10, h = 5, f1 = 12, f0 = 8, f2 = 4, the mode is —
💡 Hint:
4/12 × 5.
Explanation:
35/3.
3
If a = 20, h = 5 and Σfiui/Σfi = 2, the mean is ______.
💡 Hint:
30.
Explanation:
20 + 10.
4
Make the classes 2-6 and 7-11 continuous. Write the width.
Model answer (board format)
The gap is 1, half is 0.5. Classes 1.5-6.5 and 6.5-11.5. The width is 5.
Check your answer:
5
The mean is 18 and the mode is 24. Find the empirical median. Then write why the formula median may differ.
Model answer (board format)
3 median = 24 + 36 = 60, so the median is 20. This is an empirical estimate. The median from the table may differ because it uses cumulative frequency.
Check your answer:
6
Assertion (A): Exercise 13.1 is about the mean.
Reason (R): The section before it teaches direct, assumed-mean and step-deviation methods.
Explanation:
Both are true and R explains A.
CBSE-style questions
0/6These are competency-based practice questions. They are not a copy of any year’s paper.
1
A student writes 10 as the mark of 0-10. The correct mark is —
💡 Hint:
The average of both limits.
Explanation:
5.
2
A student puts the cumulative frequency of the whole median class in place of cf. If n/2 = 10 and the previous total is 5, the correct subtraction is —
💡 Hint:
cf is the previous one.
Explanation:
10 − 5.
3
Assertion (A): Drawing an ogive is the first job of Exercise 13.1.
Reason (R): The note to the reader says classes should be continuous before an ogive.
Explanation:
A is false, 13.1 is the mean. R is true.
4
Assertion (A): Step deviation multiplies by h again.
Reason (R): While making ui, (xi − a) was divided by h.
Explanation:
Both are true and R explains A.
5
A student gets 18, 19 and 20 from the three methods. Is that possible according to the book? What will you check?
Model answer (board format)
No. The three means are one number. Check the sums of fiui or fidi and the return of h.
Check your answer:
6
If the mode is 24.375 and the mean is 18 in one table, does the empirical relation tell you to force them equal?
Model answer (board format)
No. The relation estimates the median, and even that is not a firm rule. The mode and the mean may stay different.
Check your answer:
🏛️ Board exam corner — Bihar Board (BSEB)— CBSE
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🧠 What you learned + equation sheet
What you learned
- The class mark is the average of the two limits.
- The three methods for the mean give the same answer.
- The modal class has the greatest frequency.
- The median class is the one where the cumulative frequency reaches n/2.
- Make the classes continuous before the mode and the median.
- 3 median = mode + 2 mean is an empirical relation.
| What | Keep this |
|---|---|
| Class mark | (निचली + ऊपरी) / 2 |
| Direct mean | Σfixi / Σfi |
| Assumed mean | a + Σfidi / Σfi |
| Step deviation | a + (Σfiui / Σfi) × h |
| Mode | l + ((f1−f0)/(2f1−f0−f2)) × h |
| Median | l + ((n/2 − cf)/f) × h |
The notes are original writing. The textbook was used only for activity order and numbers. “Verified” will be used only on a question that has a source page.