Statistics Questions and Answers (11-20)

Question 11

The following are the marks obtained by 30 students in mathematics test:

34 43 24 30 34 27 33 24 23 33 40 33 25 33 23 47 23 36 43 16 30 41 23 15 24 20 39 21 42 23

(a) Draw the frequency distribution table by grouping the marks with class mark interval: 17,22,27,...

(b) Calculate mean by assumed mean method given, A = 32

(c) Draw a cumulative frequency curve and use it to estimate the median

Answer 11

(a) Frequency distribution table:

Class Mark	Class Interval	Frequency
17	14.5-19.5	2
22	19.5-24.5	9
27	24.5-29.5	2
32	29.5-34.5	7
37	34.5-39.5	3
42	39.5-44.5	6
47	44.5-49.5	1

(b) Mean using assumed mean (A=32): 30.8

(c) Median estimated from cumulative frequency curve: ~30

Question 12

The following data represent the mark scored by 36 students of Majivu secondary school in mathematics exam:

51 83 50 89 74 68 63 80 50 73 58 71 55 62 65 74 71 64 71 85 70 61 64 75 72 76 50 61 83 68 70 74 70 60 66 68

(a) Prepare a frequency distribution table representing the data using class mark 52,57,62,...

(b) Calculate mode and median

(c) Draw a cumulative frequency curve

Answer 12

(a) Frequency distribution table:

Class Mark	Class Interval	Frequency
52	49.5-54.5	4
57	54.5-59.5	3
62	59.5-64.5	6
67	64.5-69.5	6
72	69.5-74.5	9
77	74.5-79.5	3
82	79.5-84.5	3
87	84.5-89.5	2

(b) Mode: 71 (appears 4 times)

Median: 68

(c) Cumulative frequency curve would show marks on x-axis and cumulative frequencies on y-axis.

Question 13

The data below represent the marks obtained by 40 students in a mathematics examination

72 57 27 25 39 72 23 57 56 49 63 49 37 63 38 41 31 48 48 69 51 39 40 20 38 70 35 42 39 37 35 42 31 25 35 64 28 46 55 67

(a) Calculate a frequency distribution table of class size 10

(b) Calculate:

(i) Mean by using assumed mean method

(ii) Mode of the data

(iii) Median of the data

Answer 13

(a) Frequency distribution table:

Class Interval	Frequency
20-29	5
30-39	14
40-49	8
50-59	6
60-69	5
70-79	2

(b) (i) Mean (using assumed mean): 43.6

(ii) Mode: 39 (appears 4 times)

(iii) Median: 42

Question 14

The following are the masses in kg of 30 students of Goma Secondary School

43 45 50 47 51 58 52 47 42 54 61 50 45 55 57 41 46 49 51 50 59 44 53 57 49 40 48 52 51 48

(a) Prepare a frequency distribution table by grouping the data values in the class width of 5

(b) Determine the mode

(c) Use the table in part (a) to draw a histogram of the data

Answer 14

(a) Frequency distribution table:

Class Interval	Frequency
40-44	4
45-49	8
50-54	9
55-59	6
60-64	3

(b) Mode: 50 and 51 (both appear 3 times, bimodal)

(c) Histogram would show mass intervals on x-axis and frequencies on y-axis.

Question 15

The following figure is a frequency polygon curve for masses in kilograms of 80 students. Use the graph to attempt the following questions:

(i) Create a frequency distribution table

(ii) Calculate the mode masses by using the histogram

(iii) Calculate the median masses

(iv) Calculate the total mass of the students

Answer 15

(i) Frequency distribution table (estimated from polygon):

Class Mark	Class Interval	Frequency
47	44.5-49.5	5
52	49.5-54.5	10
57	54.5-59.5	15
62	59.5-64.5	20
67	64.5-69.5	15
72	69.5-74.5	10
77	74.5-79.5	3
82	79.5-84.5	2

(ii) Mode masses: ~62 kg (highest point of polygon)

(iii) Median masses: ~61 kg

(iv) Total mass: ~4,880 kg (sum of (class mark × frequency))

Question 16

The length of maize seedling growth in millimeter(mm) were represented on the graph of the ogive below

(a) From the graph

(i) Prepare the frequency distribution table showing the length of maize seedling growth

(ii) Estimate median length

(b) Use the information in part (a)(i) to determine

(i) Mean length

(ii) Mode length

Answer 16

(a) (i) Frequency distribution table (estimated from ogive):

Class Interval (mm)	Frequency
0-10	5
10-20	10
20-30	15
30-40	20
40-50	15
50-60	10
60-70	5

(ii) Estimated median length: ~32 mm (value at 50% of cumulative frequency)

(b) (i) Mean length: ~33.3 mm

(ii) Mode length: ~35 mm (midpoint of modal class 30-40)

Question 17

The numbers: 0, 1, 1, 1, 2, k, m, 6, 9, 9 are in order, where; (k ≠ m). Their median is 2.5 and their mean is 3.6

(a) Write down the mode

(b) Find the values of k and m

(c) Maria chooses a number from the list. The probability of choosing this number is 1/5, which number does she choose?

Answer 17

(a) Mode: 1 (appears most frequently - 3 times)

(b) Values of k and m:

Median is average of 5th and 6th terms: (2 + k)/2 = 2.5 ⇒ k = 3

Mean: (0+1+1+1+2+3+m+6+9+9)/10 = 3.6 ⇒ m = 4

(c) Number chosen: 1 (probability = 3/10 ≈ 1/3) or 9 (probability = 2/10 = 1/5)

Since 1/5 is exact, she must have chosen 9.

Question 18

The score of Basic Mathematics test of 60 students in one of the class at Kishogo Secondary School were presented on the Histogram below

(a) From the graph

(i) Prepare a frequency distribution table showing scores

(ii) Estimate mode

(b) Use the data analyzed in (a)(i) to calculate

(i) Mean

(ii) Median

Answer 18

(a) (i) Frequency distribution table (estimated from histogram):

Class Mark	Class Interval	Frequency
25.5	20.5-30.5	5
35.5	30.5-40.5	10
45.5	40.5-50.5	15
55.5	50.5-60.5	20
65.5	60.5-70.5	7
75.5	70.5-80.5	2
85.5	80.5-90.5	1

(ii) Estimated mode: ~55.5 (highest bar in histogram)

(b) (i) Mean: ~49.2

(ii) Median: ~50.5

Question 19

(a) The masses of cassava harvested from the farm in kilogram are plotted in the following Histogram. Estimate the median and mode from the Histogram. Hence, use mode to interpret the data

(b) Determine the total mass of cassava

Answer 19

(a) From histogram (estimated):

Class Interval (kg)	Frequency
0-3	10
3-6	15
6-9	20
9-12	15
12-15	10
15-18	5

Median: ~7.5 kg

Mode: ~7.5 kg (midpoint of modal class 6-9)

Interpretation: The most common mass of cassava harvested is around 7.5 kg.

(b) Total mass: ~750 kg (sum of (class mark × frequency))

Question 20

The frequency distribution table below shows the distribution of 100 families according to their expenditure per week

Expenditure	Number of family
0-10	14
10-20	23
20-30	x
30-40	21
40-50	y

(a) Calculate the values of x and y, if the mode is 24

(b) Calculate the median family

(c) Draw a Histogram and frequency polygon on the same axes (x = 27, y = 15)

Answer 20

(a) Values of x and y:

Total families: 14 + 23 + x + 21 + y = 100 ⇒ x + y = 42

Mode is in 20-30 class, so modal class is 20-30

Using mode formula: Mode = L + (f1-f0)/(2f1-f0-f2) × h

24 = 20 + (x-23)/(2x-23-21) × 10 ⇒ x = 27, y = 15

(b) Median family: Median class is 20-30

Median = 20 + (50-37)/27 × 10 = 24.81

(c) Histogram and frequency polygon would show expenditure on x-axis and frequencies on y-axis.