Compute the mean for following data: Class 1 - 3 3 - 5 5 - 7 7 - 9 Frequency 12 22 27 19

The given data is shown as follows: Class Frequency Class mark ' ( X i ) ' ' f i X i ' 1 - 3 12 2 24 3 - 5 22 4 88 5 - 7 27 6 162 7 - 9 19 8 152 Total ∑ f i = 80 ∑ f i X i = 426 The mean of given data is given by x = ∑ f i x i ∑ f i = 426 80 = 5 . 325 Thus, the mean of the following data is 5 . 325 .

Find the mean using direct method: Class 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 7 5 6 12 8 2

Class Frequency ' ( f i ) ' Mid value ' ( x i ) ' ' f i x i ' 0-10 7 5 35 10-20 5 15 75 20-30 6 25 150 30-40 12 35 420 40-50 8 45 360 50-60 2 55 110 ' ∑ f i = 40 ' ' ∑ ( f i x i ) = 1150 ' ∴ Mean , x = ' ( ∑ ( f i x i ) ) / ( ∑ f i ) ' = 1150 / 40 = 28 . 75 ∴ x = 28 . 75

Find the mean of the following data, using direct method: Class 0 - 100 100 - 200 200 - 300 300 - 400 400 - 500 Frequency 6 9 15 12 8

Class Frequency ( f i ) Mid values ( x i ) ( f i × x i ) 0 - 100 6 50 300 100 - 200 9 150 1350 200 - 300 15 250 3750 300 - 400 12 350 4200 400 - 500 8 450 3600 ∑ f i = 50 ∑ ( f i × x i ) = 13200 ∴ Mean = ∑ ( f i x × x i ) ∑ f i = 13200 50 = 264

Using an appropriate method, find the mean of the following frequency distribution: Class 84 - 90 90 - 96 96 - 102 102 - 108 108 - 114 114 - 120 Frequency 8 10 16 23 12 11 Which method did you use, and why?

Class Frequency ' ( f i ) ' Mid value ' ( x i ) ' ' ( f i x i ) ' 84 - 90 8 87 696 90 - 96 10 93 930 96 - 102 16 99 1584 102 - 108 23 105 2415 108 - 114 12 111 1332 114 - 120 11 117 1287 Total ' ∑ f i ' = 80 ' ∑ f i x i = 8244 ' The mean of the data is given by, x ¯ = ' ( s u m f i x i ) / ( s u m f i ) ' = 8244 80 = 103 . 05 Thus, the mean of the following data is 103 . 05 . I used direct method because the values of items are simply summed and divided by the number of observations.

If the mean of the following frequency distribution is 24 , find the value of p . Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 3 4 p 3 2

The given data is shown as follows: Class Frequency ' ( f i ) ' Mid values ' ( x i ) ' ' ( f i x i ) ' 0 - 10 3 5 15 10 - 20 4 15 60 20 - 30 p 25 25 p 30 - 40 3 35 105 40 - 50 2 45 90 Total ' s u m f i = 12 + p ' ' s u m f i x i = 270 + 25 p ' The mean of the given data is given by, x = ∑ f i x i ∑ f i ⇒ 24 = ( 270 + 25 p ) 12 + p ⇒ 24 ( 12 + p ) = 270 + 25 p ⇒ 288 + 24 p = 270 + 25 p ⇒ 25 p - 24 p = 288 - 270 ⇒ p = 18 Hence, the value of p is 18 .

The mean of following frequency distribution is 54 . Find the value of p . Class 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 Frequency 7 p 10 9 13

The given data is shown as follows: Class Frequency ( f i ) Class mark ( x i ) f i x i 0 - 20 7 10 70 20 - 40 p 30 30 p 40 - 60 10 50 500 60 - 80 9 70 630 80 - 100 13 90 1170 Total ∑ f i = 39 + p ∑ f i x i = 2370 + 30 p The mean of the given data is given by, x = ∑ i f i x i ∑ i f i ⇒ 54 = 2370 + 30 p 39 + p ⇒ 54 39 + p = 2370 + 30 p ⇒ 2106 + 54 p = 2370 + 30 p ⇒ 54 p - 30 p = 2370 - 2106 ⇒ 24 p = 264 ⇒ p = 11 Hence, the value of p is 11 .

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If the mean of $25$ observations is $27$ and each observation is decreased by $7$ , what will be new mean?

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

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Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18A>Q 3

Compute the mean for following data:

Class	$1 - 3$	$3 - 5$	$5 - 7$	$7 - 9$
Frequency	$12$	$22$	$27$	$19$

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IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18A>Q 4

Find the mean using direct method:

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	7	5	6	12	8	2

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IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18A>Q 5

Find the mean of the following data, using direct method:

Class

25 - 35

35 - 45

$45 - 55$

55 - 65

65 - 75

Frequency

6

10

8

4

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Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18A>Q 6

Find the mean of the following data, using direct method:

Class	$0 - 100$	$100 - 200$	$200 - 300$	$300 - 400$	$400 - 500$
Frequency	$6$	$9$	$15$	$12$	$8$

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10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18A>Q 7

Using an appropriate method, find the mean of the following frequency distribution:

Class	$84 - 90$	$90 - 96$	$96 - 102$	$102 - 108$	$108 - 114$	$114 - 120$
Frequency	$8$	$10$	$16$	$23$	$12$	$11$

Which method did you use, and why?

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10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18A>Q 8

If the mean of the following frequency distribution is $24$ , find the value of $p$ .

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$3$	$4$	$p$	$3$	$2$

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10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 18 - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive>Exercise 18A>Q 9

The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is $₹ 18$ , find the missing frequency $f$ .

Daily pocket allowance (in Rs.)	$11 - 13$	$13 - 15$	$15 - 17$	$17 - 19$	$19 - 21$	$21 - 23$	$23 - 25$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

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10th CBSE

IMPORTANT

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

The mean of following frequency distribution is $54$ . Find the value of $p$ .

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$7$	$p$	$10$	$9$	$13$

If the mean of 25 observations is 27 and each observation is decreased by 7, what will be new mean?

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

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If the mean of $25$ observations is $27$ and each observation is decreased by $7$ , what will be new mean?