Find the mean of the following frequency distribution using step-deviation method: Class 84 - 90 90 - 96 96 - 102 102 - 108 108 - 114 114 - 120 Frequency 15 22 20 18 20 25

For step-deviation method, we prepare the following table: Class interval Frequency f i Mid-value x i u i = x i - A h = x i - 99 6 f i u i 84 - 90 15 87 - 2 - 30 90 - 96 22 93 - 1 - 22 96 - 102 20 99 = A 0 0 102 - 108 18 105 1 18 108 - 114 20 111 2 40 114 - 120 25 117 3 75 ∑ f i = 120 ∑ f i u i = 81 Thus, A = 99 , h = 6 , ∑ f i = 120 and ∑ f i u i = 81 Mean = A + h × ∑ f i u i ∑ f i = 99 + 6 × 81 120 = 99 + 4 . 05 = 103 . 05

Find the mean, median and mode of the following data: Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Frequency 6 8 10 15 5 4 2

We prepare the following table: Class interval Frequency f i Mid-value x i f i × x i Cumulative frequency 0 - 10 6 5 30 6 10 - 20 8 15 120 14 20 - 30 10 25 250 24 30 - 40 15 35 525 39 40 - 50 5 45 225 44 50 - 60 4 55 220 48 60 - 70 2 65 130 50 ∑ f i = 50 ∑ f i x i = 1500 Mean: Mean = ∑ f i x i ∑ f i = 1500 50 = 30 Median: N = 50 ⇒ N 2 = 25 The cumulative frequency just greater than 25 is 39 Hence, median class is 30 - 40 ∴ l = 30 , h = 10 , f = 15 , c f = c f of preceding class = 24 Now, Median = l + h × N 2 - c f f = 30 + 10 × 25 - 24 15 = 30 + 0 . 67 = 30 . 67 Mode: Maximum frequency = 15 Hence, modal class is 30 - 40 Now, Mode = x k + h f k - f k - 1 2 f k - f k - 1 - f k + 1 = 30 + 10 15 - 10 2 15 - 10 - 5 = 30 + 3 . 33 = 33 . 33

Draw 'less than ogive' more than ogive' on a single graph paper and hence find the median of the following data: Class interval 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 Frequency 2 12 2 4 3 4 3

Less than series Class interval Frequency Less than 10 2 Less than 15 14 Less than 20 16 Less than 25 20 Less than 30 23 Less than 35 27 Less than 40 30 We plot the points 10 , 2 , 15 , 14 , 20 , 16 , 25 , 20 , 30 , 23 , 35 , 27 and 40 , 30 to get less than ogive. More than type Class Interval Frequency More than 5 30 More than 10 28 More than 15 16 More than 20 14 More than 25 10 More than 30 7 More than 35 3 Plot the points 5 , 30 , 10 , 28 , 15 , 16 , 20 , 14 , 25 , 10 , 30 , 7 , 35 , 3 for more than type The two curves intersect at L . Draw L M ⊥ O X Thus, median = L M = 16

The production yield per hectare of wheat of some farms of a village are given in the following table: Production yield (in kg/ha) 40 - 45 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 80 - 85 Number of farms 1 9 15 18 40 26 16 14 10 Draw a less than type ogive and a more than type ogive for this data

Class interval Less than 45 1 Less than 50 10 Less than 55 25 Less than 60 43 Less than 65 83 Less than 70 109 Less than 75 125 Less than 80 139 Less than 85 149 We plot the points 45 , 1 , 50 , 10 , 55 , 25 , 60 , 43 , 65 , 83 , 35 , 27 , 70 , 109 , 75 , 125 , 80 , 139 and 85 , 149 to get less than ogive More than Series Class interval More than 40 149 More than 45 148 More than 50 139 More than 55 124 More than 60 106 More than 65 66 More than 70 40 More than 75 24 More than 80 10 We plot the points 40 , 149 , 45 , 148 , 50 , 139 , 55 , 124 , 60 , 106 , 65 , 66 , 70 , 40 , 75 , 24 and 80 , 10 to get more than ogive

The following table gives the marks obtained by 50 students in a class test Marks 11 - 15 16 - 20 21 - 25 26 - 30 31 - 35 36 - 40 41 - 45 46 - 50 Number of students 2 3 6 7 14 12 4 2 Calculate the mean, median and mode for the above data

We make the classes exclusive Class interval Frequency f i Mid-value x i f i x i Cumulative frequency 10 . 5 - 15 . 5 2 13 26 2 15 . 5 - 20 . 5 3 18 54 5 20 . 5 - 25 . 5 6 23 138 11 25 . 5 - 30 . 5 7 28 196 18 30 . 5 - 35 . 5 14 33 462 32 35 . 5 - 40 . 5 12 38 456 44 40 . 5 - 45 . 5 4 43 172 48 45 . 5 - 50 . 5 2 48 96 50 ∑ f i = 50 ∑ f i x i = 1600 Mean: Mean = ∑ f i x i ∑ f i = 1600 50 = 32 Median: N = 50 ⇒ N 2 = 25 The cumulative frequency just greater than 25 is 32 Hence, the median class is 30 . 5 - 35 . 5 ∴ l = 30 . 5 , h = 5 , f = 14 , c f = c f of preceding class = 18 Now, median = l + h × N 2 - c f f = 30 . 5 + 5 × 25 - 18 14 = 30 . 5 + 2 . 5 = 33 Mode: Maximum frequency = 14 Hence, modal class is 30 . 5 - 35 . 5 Now, Mode = x k + h f k - f k - 1 2 f k - f k - 1 - f k + 1 = 30 . 5 + 5 14 - 7 2 14 - 7 - 12 = 30 . 5 + 3 . 8 = 34 . 4

MEDIUM

10th CBSE

IMPORTANT

Earn 100

For the following distribution draw a 'less than type' ogive and from the curve find the median.

Marks obtained Less than $20$ Less than $30$ Less than $40$ Less than $50$ Less than $60$ Less than $70$ Less than $80$ Less than $90$ Less than $100$

Number of students $2$ $7$ $17$ $40$ $60$ $82$ $85$ $90$ $100$

Important Questions on Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>TEST YOURSELF>Q 16

The median value for the following frequency distribution is $35$ and the sum of all frequencies is $170$ . Using the formula for median, find the missing frequencies.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$10$	$20$	?	$40$	?	$25$	$15$

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>TEST YOURSELF>Q 17

Find the missing frequencies $f_{1}$ and $f_{2}$ in the table given below, it being given that the mean of the given frequency distribution is $50$ .

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	Total
Frequency	$17$	$f_{1}$	$32$	$f_{2}$	$19$	$120$

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>TEST YOURSELF>Q 18

Find the mean of the following frequency distribution using step-deviation method:

Class	$84 - 90$	$90 - 96$	$96 - 102$	$102 - 108$	$108 - 114$	$114 - 120$
Frequency	$15$	$22$	$20$	$18$	$20$	$25$

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>TEST YOURSELF>Q 19

Find the mean, median and mode of the following data:

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$6$	$8$	$10$	$15$	$5$	$4$	$2$

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>TEST YOURSELF>Q 20

Draw 'less than ogive' more than ogive' on a single graph paper and hence find the median of the following data:

Class interval	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$
Frequency	$2$	$12$	$2$	$4$	$3$	$4$	$3$

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>TEST YOURSELF>Q 21

The production yield per hectare of wheat of some farms of a village are given in the following table:

Production yield (in kg/ha)	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$
Number of farms	$1$	$9$	$15$	$18$	$40$	$26$	$16$	$14$	$10$

Draw a less than type ogive and a more than type ogive for this data

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>TEST YOURSELF>Q 22

The following table gives the marks obtained by $50$ students in a class test

Marks	$11 - 15$	$16 - 20$	$21 - 25$	$26 - 30$	$31 - 35$	$36 - 40$	$41 - 45$	$46 - 50$
Number of students	$2$	$3$	$6$	$7$	$14$	$12$	$4$	$2$

Calculate the mean, median and mode for the above data

Marks obtained	Less than $20$	Less than $30$	Less than $40$	Less than $50$	Less than $60$	Less than $70$	Less than $80$	Less than $90$	Less than $100$
Number of students	$2$	$7$	$17$	$40$	$60$	$82$	$85$	$90$	$100$

For the following distribution draw a 'less than type' ogive and from the curve find the median. Marks obtained Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 Less than 90 Less than 100 Number of students 2 7 17 40 60 82 85 90 100

Important Questions on Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

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