Statistics

Which statement best summarizes the chapter "Statistics"?

1. The chapter studies only arithmetic calculations.
2. The chapter introduces grouped frequency distributions, cumulative frequencies, ogives, and the calculation of the median using the standard statistical formula, enabling students to analyze and interpret real-life data effectively.
3. The chapter focuses only on circles.
4. The chapter has no practical applications.

Which statement about cumulative frequency is correct?

1. It always decreases.
2. It is obtained by successively adding frequencies.
3. It is always equal to one.
4. It is smaller than every frequency.

Which chapter mainly introduces the calculation of the median for grouped data?

1. Probability
2. Statistics
3. Surface Areas and Volumes
4. Trigonometry

Which quantity is NOT directly required in the median formula?

1. Lower boundary
2. Frequency of the median class
3. Radius
4. Class width

Which measure divides the observations into two equal parts?

1. Mean
2. Median
3. Mode
4. Range

If the total frequency is 80, then N/2 equals:

1. 20
2. 30
3. 40
4. 80

If the frequencies are 5, 8, 7, and 10, the total frequency is:

1. 20
2. 25
3. 30
4. 35

Which of the following is essential before applying the median formula?

1. Finding the highest frequency
2. Calculating cumulative frequencies
3. Drawing a pie chart
4. Finding the range

Which graph is commonly associated with finding the median graphically?

1. Bar Graph
2. Histogram
3. Ogive
4. Pie Chart

The class width in the median formula is represented by:

1. f
2. h
3. N
4. cf

What does "cf" represent in the median formula?

1. Class Frequency
2. Cumulative Frequency before the Median Class
3. Central Frequency
4. Continuous Frequency

The total frequency of a grouped frequency distribution is represented by:

1. h
2. l
3. N
4. cf

Which formula is used to calculate the median of grouped data?

1. Mean = Sum of observations / Number of observations
2. Median = l + [(N/2 − cf)/f] × h
3. Mode = Highest frequency
4. Range = Highest − Lowest

The median class is the class interval whose cumulative frequency is:

1. Equal to the highest frequency
2. First greater than or equal to N/2
3. Equal to zero
4. Always the last class

Which measure of central tendency is the primary focus of Class 10 Statistics?

1. Mean only
2. Median of grouped data
3. Mode only
4. Range

If mean of 8 numbers is 25, what is their sum?

1. 150
2. 175
3. 200
4. 225

Mode of 6, 6, 7, 8, 8, 8, 9 is:

1. 6
2. 7
3. 8
4. 9

Median of data 2, 6, 8, 10, 12, 14, 16 is:

1. 8
2. 10
3. 12
4. 14

If all observations are same (5, 5, 5, 5), what is mean?

1. 0
2. 5
3. 10
4. 20

Find range of: 12, 45, 20, 30, 10

1. 25
2. 30
3. 35
4. 40

Mean of 10, 20, 30, 40, x is 30. Find x.

1. 40
2. 50
3. 60
4. 70

Find median of 5, 1, 9, 3, 7

1. 3
2. 5
3. 7
4. 9

Find mode of: 1, 2, 2, 3, 4, 4, 4, 5

1. 2
2. 3
3. 4
4. 5

If mean of 5 numbers is 20, find their total sum.

1. 80
2. 90
3. 100
4. 110

Find mean of first five natural numbers.

1. 2
2. 3
3. 4
4. 5

Find median of: 10, 20, 30, 40, 50, 60

1. 25
2. 30
3. 35
4. 40

Mean of 4, 8, x, 12, 16 is 10. Find x.

1. 8
2. 10
3. 12
4. 14

Find mode of: 2, 3, 3, 5, 7, 3, 9

1. 2
2. 3
3. 5
4. 7

Find the median of: 3, 7, 9, 15, 21

1. 7
2. 9
3. 15
4. 10

Find the mean of the following data: 2, 4, 6, 8, 10

1. 5
2. 6
3. 7
4. 8

Sum of 15 numbers is 435. Mean is

1. 30
2. 28
3. 29
4. none

Mean of (a+b)/2 and (a–b)/2 is

1. (a+b)/4
2. (a–b)/4
3. a/2
4. none

Marks 140,153,148,150,154. Mean is

1. 129
2. 139
3. 149
4. 159

Mean of first six prime numbers is

1. 6.8
2. 3.6
3. 5.6
4. 5.2

Mean of first 5 multiples of 5 is

1. 14
2. 16
3. 13
4. 15

Averages: A&B=25, B&C=28, C&A=21. Average of A,B,C is

1. 23.66
2. 25.66
3. 26.66
4. 24.66

Sum of deviations from 50 is –10, from 46 is 70. Mean is

1. 49.75
2. 49.5
3. 49
4. none

Average age of 5 teachers=28. One excluded, mean reduces by 2. Age of excluded teacher is

1. 26 years
2. 33 years
3. 36 years
4. none

Girls avg=68, boys avg=62, class avg=64. Ratio of girls to boys is

1. 1:2
2. 1:1
3. 2:3
4. 3:5

Mean of 20 numbers=15. If 2 added to first 10, new mean is

1. 13
2. 30
3. 16
4. 17

Median found graphically from

1. Histogram
2. Frequency polygon
3. Frequency polygon
4. Ogive

Number of students who got below/equal to 50% marks (from ogive)

1. 5
2. 10
3. 15
4. 20

If 13 replaced by 28 in data 24,17,13,24,26,20,26,30,8,41,24. New median is

1. 20
2. 17
3. 13
4. 24

Mid value 60, class size 10. Upper and lower limits are

1. 65 & 55
2. 45 & 55
3. 35 & 45
4. 25 & 35

Ogive of 100 students marks. Median mark (approximately) is

1. 40
2. 50
3. 55
4. 60

Which is NOT a measure of central tendency

1. Mean
2. Median
3. Mode
4. Standard deviation

Mean of discrete frequency distribution is given by

1. Σfx/Σf
2. Σf/Σx
3. Σfx
4. Σx/n

Mean of 9 observations is 36. First 5 mean=32, last 5 mean=39. 5th observation is

1. 31
2. 43
3. 28
4. 37

Arithmetic mean of 1,2,3,...n is

1. (n+1)/2
2. n/2
3. (n–1)/2
4. n/2+1

Class size of class interval 20–35 is

1. 5
2. 10
3. 20
4. 15

Class mark of class interval 20–60 is

1. 30
2. 40
3. 50
4. 20

Mid-value of class interval is 45, class size=10. Upper and lower limits are

1. 45 & 35
2. 60 & 40
3. 50 & 40
4. 40 & 30

Median from class distribution 5–10(5),10–15(6),15–20(15),20–25(10)...

1. 20.5
2. 19.511
3. 18.5
4. 15.5

If mode=25 for: 15,20,25,18,14,15,25,15,18,16,20,25,20,x,18. Value of x is

1. 20
2. 15
3. 14
4. 25

Mode of: 120,110,130,110,120,140,130,120,140,120

1. 140
2. 120
3. 130
4. 110

Median from frequency distribution x={1..9}, f={8,10,11,16,20,25,15,9,6}

1. 9
2. 6
3. 8
4. 5

Median of wages: Rs 20,25,17,18,8,15,22,11,9,14

1. 17
2. 19
3. 16
4. 15

Mean of distribution=1.46. Find missing frequencies f1,f2 where total=200.

1. 78 and 40
2. 76 and 38
3. 90 and 30
4. 20 and 80

Mean of 6 numbers is 43. One excluded, mean of remaining is 41. Excluded number is

1. 53
2. 84
3. 12
4. 78

Bus: P to Q at 60kmph, Q to P at 90kmph. Average speed is

1. 72 kmph
2. 30 kmph
3. 150 kmph
4. 75 kmph

Empirical formula for mode is

1. Mode=2median–3mean
2. Mode=3median–2mean
3. Mode=5median–4mean
4. Mode=4median–5mean

Mid points of class intervals are called

1. mean
2. range
3. median
4. class-mark

Family sizes 1–3(7), 3–5(8), 5–7(2), 7–9(2), 9–11(1). Mode is

1. 5.6
2. 3.28
3. 7.59
4. 8.29

Find mean of grouped data: 0–10(5),10–20(18),20–30(15),30–40(16),40–50(6)

1. 26
2. 28
3. 25
4. 30

Mean of data is 12, find p: x={4,8,p,16,20}, f={5,3,12,5,4}

1. 10
2. 12
3. 14
4. 15