Statistics Questions and Answers (1-10)
Question 1
In a certain school, the scores of 24 students in one of the Chemistry tests were as follows:
49, 64, 38, 46, 60, 68, 46, 42, 62, 38, 68, 57, 63, 76, 72, 73, 51, 55, 66, 63, 58, 47, 59 and 54
(a) Summarize the above data in a frequency distribution table using class size 5 and lowest limit of 35.
(b) Determine median score (Give your answer to two significant figures).
(c) Determine the score obtained by many students (Write your answer in two significant figures).
Answer 1
(a) Frequency distribution table:
| Class Interval | Frequency |
|---|---|
| 35-39 | 3 |
| 40-44 | 2 |
| 45-49 | 4 |
| 50-54 | 3 |
| 55-59 | 4 |
| 60-64 | 4 |
| 65-69 | 2 |
| 70-74 | 2 |
| 75-79 | 1 |
(b) Median score: 58
(c) Mode (score obtained by many students): 46 and 63 (both appear twice, bimodal)
Question 2
Display the results below in a histogram using 10 class interval size whereby the first class mark x be 5.5 and the last class mark x be 75.5
15 25 30 40 60 40 25 15 15 20 30 75 20 30 20 15 10 20 35 45 35 30 20 10 55 25 10 5 15 30 30 40 15 5 10 45 30 20 20 15 65 40 15 5 45 20 30 20 30 10
Answer 2
Histogram data (class intervals and frequencies):
| Class Interval | Class Mark | Frequency |
|---|---|---|
| 0.5-10.5 | 5.5 | 7 |
| 10.5-20.5 | 15.5 | 15 |
| 20.5-30.5 | 25.5 | 16 |
| 30.5-40.5 | 35.5 | 7 |
| 40.5-50.5 | 45.5 | 5 |
| 50.5-60.5 | 55.5 | 1 |
| 60.5-70.5 | 65.5 | 2 |
| 70.5-80.5 | 75.5 | 1 |
Note: A histogram would be drawn with these class intervals on the x-axis and frequencies on the y-axis.
Question 3
By grouping the data below using 10 class interval size with class mark of 5.5, 15.5, 25.5, ... find the mean, median and mode using assumed mean method where applicable taking A = 45.5.
15 25 30 40 60 40 25 15 15 20 30 75 20 30 20 15 10 20 35 45 35 30 20 10 55 25 10 5 15 30 30 40 15 5 10 45 30 20 20 15 65 40 15 5 45 20 30 20 30 10
Answer 3
Using class marks: 5.5, 15.5, 25.5, 35.5, 45.5, 55.5, 65.5, 75.5
Mean (using assumed mean method, A = 45.5): 28.9
Median: 25.5 (middle value of the ordered data set)
Mode: 15.5 (most frequent class mark)
Question 4
The marks below were obtained by 32 students in a civics test.
52 48 37 45 38 29 32 46 50 42 35 32 28 34 37 64 42 37 54 36 48 52 58 71 67 48 62 54 57 34 64 58
a) Prepare a frequency distribution table by grouping the marks using the class marks: 26.5, 32.5, 38.5, ...
b) Determine the mode from the histogram.
c) Calculate: i. the mean mark ii. The median mark
d) Prepare the pie chart from the frequency distribution table prepared in (a) above
Answer 4
a) Frequency distribution table:
| Class Mark | Class Interval | Frequency |
|---|---|---|
| 26.5 | 23.5-29.5 | 2 |
| 32.5 | 29.5-35.5 | 5 |
| 38.5 | 35.5-41.5 | 6 |
| 44.5 | 41.5-47.5 | 5 |
| 50.5 | 47.5-53.5 | 5 |
| 56.5 | 53.5-59.5 | 5 |
| 62.5 | 59.5-65.5 | 3 |
| 68.5 | 65.5-71.5 | 1 |
b) Mode from histogram: Approximately 38.5 (highest bar in the histogram)
c) i. Mean mark: 47.2
ii. Median mark: 46.5
d) Pie chart would show the percentage distribution of marks across the class intervals.
Question 5
Mr. Ndukeki timed all the phone calls his lovely wife made during august 2020. This list gives the times in minutes and seconds (e.g. 1.23 stands for 1 minute and 23 seconds).
6.24 5.12 3.04 6.26 5.01 3.52 4.14 7.19 6.34 2.05 5.40 4.48 5.17 2.58 3.48 2.00 1.46 0.48 6.06 0.50 2.45 6.00 3.03 4.24 3.34 1.20 7.48 2.44 2.03 3.45 3.53 1.34 0.45 3.54 5.40 4.47 7.41 6.50 6.43 5.23 4.49 2.34 3.49 2.00 4.09 3.48 5.23 2.47 5.23 1.40 6.05 5.10 7.09 5.45 5.07 6.45 7.53 6.09 4.06 5.45 5.32 0.56 4.57 3.48 4.25 4.40 7.10 0.54 6.10 0.36
a) Prepare a frequency distribution table by grouping the marks using the class intervals: 0 - 0.59, 1 - 1.59, 2 - 2.59 etc.
b) Draw the histogram for this data
Answer 5
a) Frequency distribution table:
| Class Interval (minutes) | Frequency |
|---|---|
| 0 - 0.59 | 4 |
| 1 - 1.59 | 5 |
| 2 - 2.59 | 11 |
| 3 - 3.59 | 13 |
| 4 - 4.59 | 10 |
| 5 - 5.59 | 12 |
| 6 - 6.59 | 9 |
| 7 - 7.59 | 6 |
b) Histogram would show call durations on the x-axis and frequencies on the y-axis, with bars for each class interval.
Question 6
In a basic mathematics test, the following marks were awarded:
48 47 67 73 50 76 47 44 44 42 56 66 67 45 43 71 48 64 52 49 34 35 46 89 37 47 54 45 60 57 58 54 45 42 54 62 32 64 44 58
Prepare a frequency distribution table starting with 32 having class size of 10, and then find:
(i) Mean using assumed mean of 56.5
(ii) Mode of the distribution
Answer 6
Frequency distribution table:
| Class Interval | Frequency |
|---|---|
| 32-41 | 4 |
| 42-51 | 14 |
| 52-61 | 8 |
| 62-71 | 9 |
| 72-81 | 4 |
| 82-91 | 1 |
(i) Mean using assumed mean (56.5): 53.8
(ii) Mode: 45 (most frequent value)
Question 7
The data below represents the Mass in kilograms(kg) of 20 bags of maize.
67 59 52 74 69 63 62 58 70 62 73 56 68 65 70 61 64 54 62 59
(a) Construct a frequency distribution table whose class marks are 53, 58, 63, ...
(b) Use the information in the table constructed in (a) above to calculate the mean mass using the class mark of the modal class as the assumed mean.
(c) Draw a histogram and a frequency polygon on same pair of axes
Answer 7
(a) Frequency distribution table:
| Class Mark | Class Interval | Frequency |
|---|---|---|
| 53 | 50.5-55.5 | 2 |
| 58 | 55.5-60.5 | 3 |
| 63 | 60.5-65.5 | 6 |
| 68 | 65.5-70.5 | 6 |
| 73 | 70.5-75.5 | 3 |
(b) Mean using modal class (63) as assumed mean: 63.8 kg
(c) Histogram and frequency polygon would show mass intervals on x-axis and frequencies on y-axis.
Question 8
The number of patients who attended maternity clinic daily in June 2017 in a certain village was recorded as follows:
52 61 42 27 38 44 56 36 73 20 41 48 77 30 46 43 72 63 43 76 47 53 38 55 60 51 47 58 33 37
(a) Make the frequency distribution table by grouping the number of patient in the class size of 10.
(b) By using the frequency distribution table obtained in (a), calculate the mean number of patient per day
(c) Construct a pie chart for the frequency distribution obtained in part (a)
Answer 8
(a) Frequency distribution table:
| Class Interval | Frequency |
|---|---|
| 20-29 | 2 |
| 30-39 | 7 |
| 40-49 | 9 |
| 50-59 | 6 |
| 60-69 | 3 |
| 70-79 | 3 |
(b) Mean number of patients per day: 48.6
(c) Pie chart would show the percentage distribution of patients across the class intervals.
Question 9
(NECTA CSEE 2021), The following are the marks obtained by 40 students in one of the Basic mathematics examination:
48 47 57 56 71 62 46 45 50 76 58 66 48 32 89 60 42 47 54 67 64 49 37 64 67 44 45 45 42 34 47 44 73 44 58 43 54 35 54 52
(a) Prepare a frequency distribution using the information: Number of classes = 8, Size of each class = 8 and The lower limit of the first class interval = 32.
(b) Use the frequency distribution obtained in part (a) to find the actual mean, when the assumed mean is 83.5
(c) Calculate the difference between the actual mean and the median of this distributions. Hence comment on the difference obtained.
Answer 9
(a) Frequency distribution table:
| Class Interval | Frequency |
|---|---|
| 32-39 | 4 |
| 40-47 | 11 |
| 48-55 | 9 |
| 56-63 | 5 |
| 64-71 | 6 |
| 72-79 | 3 |
| 80-87 | 1 |
| 88-95 | 1 |
(b) Actual mean (using assumed mean 83.5): 53.4
(c) Median: 52.5
Difference between mean and median: 0.9
Comment: The small difference suggests the data is approximately symmetric.
Question 10
The following were scores of 35 students in a Mathematics mock examination.
07 19 78 53 43 67 12 54 27 22 33 80 25 58 50 36 65 33 16 19 34 20 55 27 37 41 04 32 48 28 70 31 61 08 35
(a) Prepare a frequency distribution table using class marks 4.5, 14.5, 24.5, ...
(b) Which class interval has more students?
(c) Calculate the (i) Median mark (ii) Mode mark
Answer 10
(a) Frequency distribution table:
| Class Mark | Class Interval | Frequency |
|---|---|---|
| 4.5 | 0-9 | 3 |
| 14.5 | 10-19 | 5 |
| 24.5 | 20-29 | 6 |
| 34.5 | 30-39 | 8 |
| 44.5 | 40-49 | 3 |
| 54.5 | 50-59 | 5 |
| 64.5 | 60-69 | 2 |
| 74.5 | 70-79 | 2 |
| 84.5 | 80-89 | 1 |
(b) Class interval with most students: 30-39 (8 students)
(c) (i) Median mark: 34
(ii) Mode mark: 27 and 33 (both appear twice, bimodal)
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