Question

(a) raw data of number of t - shirts: 9 7 3 11 4 4 8 1 5 7 10 9 8 2 12 8 1 10 7 6 number of t - shirts frequency 1 to 3 4 4 to 6 7 to 9 10 to 12 (b) raw data of test scores: 23 38 32 35 11 26 33 40 25 28 17 8 19 23 34 35 20 26 38 32 test score frequency 1 to 10 11 to 20 21 to 30 31 to 40 (d) raw data of height in cm: 146 170 168 152 133 139 179 165 162 160 148 175 155 163 158 166 148 160 height (cm) frequency 130≤h<140 2 140≤h<150 150≤h<160 160≤h<170 170≤h<180 (e) raw data of distance to school in miles: 1.8 3.7 0.6 4.5 7.5 2.9 5.4 5.7 8.3 3 1.1 6.6 5.2 2.1 6 3.6 9.7 3.9 distance (miles) frequency 0≤d<2 2≤d<4 4≤d<6 6≤d<8 8≤d<10

Explanation:

Step1: Count frequencies for t - shirts data

For the range 4 - 6 in the t - shirts data: The values in this range are 4, 4, 5, 6. So the frequency is 4.
For the range 7 - 9: The values are 9, 7, 8, 9, 8, 7, 8. The frequency is 7.
For the range 10 - 12: The values are 11, 10, 12, 10. The frequency is 4.

Step2: Count frequencies for test scores data

For the range 1 - 10: There is 1 value (8), so the frequency is 1.
For the range 11 - 20: The values are 11, 17, 19, so the frequency is 3.
For the range 21 - 30: The values are 23, 26, 25, 28, 23, 20, 26, so the frequency is 7.
For the range 31 - 40: The values are 38, 32, 35, 33, 40, 34, 35, 38, 32, so the frequency is 9.

Step3: Count frequencies for height data

For the range 140 ≤ h < 150: The values are 146, 148, 148, 148. The frequency is 4.
For the range 150 ≤ h < 160: The values are 152, 155, 158. The frequency is 3.
For the range 160 ≤ h < 170: The values are 168, 165, 162, 160, 166, 160. The frequency is 6.
For the range 170 ≤ h < 180: The values are 170, 179, 175. The frequency is 3.

Step4: Count frequencies for distance data

For the range 0 ≤ d < 2: The values are 0.6, 1.1, 1.8. The frequency is 3.
For the range 2 ≤ d < 4: The values are 2.1, 2.9, 3, 3.6, 3.7, 3.9. The frequency is 6.
For the range 4 ≤ d < 6: The values are 4.5, 5.2, 5.4, 5.7. The frequency is 4.
For the range 6 ≤ d < 8: The values are 6, 6.6, 7.5. The frequency is 3.
For the range 8 ≤ d < 10: The value is 8.3, 9.7. The frequency is 2.

(a) Number of t - shirts	Frequency	(b) Test Score	Frequency	(d) Height (cm)	Frequency	(e) Distance (miles)	Frequency
4 - 6	4	11 - 20	3	140 ≤ h < 150	4	2 ≤ d < 4	6
7 - 9	7	21 - 30	7	150 ≤ h < 160	3	4 ≤ d < 6	4
10 - 12	4	31 - 40	9	160 ≤ h < 170	6	6 ≤ d < 8	3
				170 ≤ h < 180	3	8 ≤ d < 10	2

Answer:

(a) Number of t - shirts	Frequency	(b) Test Score	Frequency	(d) Height (cm)	Frequency	(e) Distance (miles)	Frequency
4 - 6	4	11 - 20	3	140 ≤ h < 150	4	2 ≤ d < 4	6
7 - 9	7	21 - 30	7	150 ≤ h < 160	3	4 ≤ d < 6	4
10 - 12	4	31 - 40	9	160 ≤ h < 170	6	6 ≤ d < 8	3
				170 ≤ h < 180	3	8 ≤ d < 10	2