CBSE/NCERT 10th Ch:14 -Statistics – Mean, Mode and Median and Ogive Guess Question for SA-1

10th Math's Chapter 14 -Statistics – Mean, Mode and Median of Grouped Data and Graphical Representation of Cumulative Frequency Distribution

"Mean, median, mode and draw cumulative frequency curves (ogives)"

The numerical representation of the ungrouped data  called measures of central tendency, namely, mean, median and mode. we shall extend the study of these three measures, i.e., mean, median and mode from ungrouped data to that of grouped data. We shall also discuss the  concept of cumulativ e frequency, the cumulative frequency distribution and how to draw cumulative frequency curves, called ogives.

Set-01

1. The class mark of the class 10 – 25 is:  (A) 17 (B) 18 (C) 17.5 (D) 15

2. Find the mean of the following frequency distribution [by assumed mean method]

Class :	0 – 6	6 – 12	12 – 18	18 – 24	24 – 30
Frequency :	7	5	10	12	6

3. Find the mode of the following frequency distribution

Class :	0 – 6	6 – 12	12 – 18	18 – 24	24 – 30
Frequency :	7	5	10	12	6

4. If the mean of the following distribution is 27, find the value of p

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency :	8	p	12	13	10

5. Find mean, and median for the following data :

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency :	8	16	36	34	6

6.  Draw ‘less than’ and ‘more than’ ogives for the following distribution:

Scores :	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80
Frequency :	8	10	14	12	4	2

7.  Find the value of f1 from the following data if its mode is 65:

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	100 – 120
Frequency	6	8	f1	12	6	5

Set-02

1. If the „less than‟ type ogive and „more than‟ type ogive intersect each other at (20.5, 15.5), then the median of the given data is : (A) 36.0 (B) 20.5 (C) 15.5 (D) 5.5           [01]

2.  Find the sum of lower limit of mediun class and the upper limit of model class : [02]

Classes :	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Frequency :	1	3	5	9	7	3

3.  Convert the following data into more than type distribution :[02]

Class :	50 – 55	55 – 60	60 – 65	65 – 70	70 – 75	75 – 80
Frequency :	2	8	12	24	38	16

4. Draw the less than type ogive for the following data and hence find the median from it.[03]

Classes :	50 – 60	60 – 70	70 – 80	80 – 90	90 – 100
Frequency :	6	5	9	12	6

5. The median of the following frequency distribution is 28.5 and the sum of all the frequencies is 60. Find the values of „p‟ and „q‟ : [03]

Classes :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Frequency :	5	p	20	15	q	5

6. Calculate the average daily income (in `) of the following data about men working in a company :[05]

Daily income (in `)	< 100	< 200	< 300	< 400	< 500
Number of men	12	28	34	41	50

7. The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean n umber of wickets by choosing a suitable method. What does the mean signify? [Hint: Here, the class size varies, and the x ^, s are large. Let us still apply the stepdeviation method with a = 200 and h = 20]

Number of wickets	20 - 60	60 - 100	100 - 150	150 – 250	250 – 350	350 - 450
Number of bowlers	7	5	16	12	2	3

8. Draw a more than ogive for the following distribution and hence find its median.

Class	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80	80 – 90
Frequency	25	15	10	6	24	12	8

 SET-03

1. Relationship among mean, median and mode is :

(A) 3 Median =Mode +2 Mean       (B) 3 Mean = Median + 2 Mode

(C) 3 Mode = Mean+2 Median       (D) Mode = 3 Mean - 2 Median

2 . Calculate the median for the following distribution :

Marks obtained	Number of students
Below 10	6
Below 20	15
Below 30	29
Below 40	41
Below 50	60
Below 60	70

3. Compute the arithmetic mean for the following data :

Marks obtained	No. of students
Less than 10	14
Less than 20	22
Less than 30	37
Less than 40	58
Less than 50	67
Less than 60	75

4. Find the missing frequencies f1 and f2 in the following frequency distribution table, if N =100 and median is 32.

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	Total
Frequency	10	f1	25	30	f2	10	100

5. For the following frequency distribution, draw a cumulative frequency curve of less than type.

Class :	200 – 250	250 – 300	300 – 350	350 – 400	400 – 450	450 – 500	500 – 550	550 – 600
Frequency:	30	15	45	20	25	40	10	15

6. The median class for the following data is

Class	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	10	12	20	22

(A) 20 - 40 (B) 40 - 60 (C) 60 - 80 (D) 80 – 100

7. Write the following frequency distribution as “more than type” and “less than type” cumulative frequency distribution.

Class :	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency :	5	15	20	23	17

8. Find the median for the following table which shows the daily wages drawn by 200 workers in a factory.

Daily wages (in Rs.)	Less than 100	Less than 200	Less than 300	Less than 400	Less than 500
No. of workers	40	82	154	184	200

9. The mean of the data in the following table is 50. Find the missing frequencies f1 and f2.

Class :	10 – 30	30 – 50	50 – 70	70 – 90	90 – 110	Total
Frequency :	90	f1	30	f2	40	200

10. Find the unknown entries a, b, c, d, e and f in the following distribution and hence find their mode.

Height (in cm) :	150–155	155–160	160–165	165–170	170–175	175–180	Total
Frequency :	12	b	10	d	e	2	50
Cumulative frequency :	a	25	c	43	48	f

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