Descriptive Stats - Chapter 2 (Session 4) - Calculations

Question 1

From Page 30, calculate the mean number of days absent for the dataset: 5, 4, 8, 1, 7, 10, 9, 3, 0, 5, 6, 15, 10, 9, 2, 16, 15, 18, 4, 12, 6, 6, 15.

Answer 1

Data: 5, 4, 8, 1, 7, 10, 9, 3, 0, 5, 6, 15, 10, 9, 2, 16, 15, 18, 4, 12, 6, 6, 15
Sum = 5 + 4 + 8 + 1 + 7 + 10 + 9 + 3 + 0 + 5 + 6 + 15 + 10 + 9 + 2 + 16 + 15 + 18 + 4 + 12 + 6 + 6 + 15 = 186
n = 23
Mean = 186 / 23 ≈ 8.09

Question 2

Determine the mode of the dataset from Page 30.

Answer 2

Most frequent: 6 and 15 (each appear 3 times)
Answer: Bimodal: 6 and 15 days

Question 2

For the same dataset, find the median number of days absent.

Answer 2

Ordered: 0, 1, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 12, 15, 15, 15, 16, 18
Median = 7 (12th value)
Answer: 7 days

Question 3

From Page 34, calculate the mean of the dataset: 7, 3, 9, 4, 8.

Answer 3

Data: 7, 3, 9, 4, 8
Sum = 7 + 3 + 9 + 4 + 8 = 31
Mean = 31 / 5 = 6.2

Question 4

Find the median of the dataset: 7, 3, 9, 4, 8 (Page 34).

Answer 4

Ordered: 3, 4, 7, 8, 9
Median = 7 (3rd value)
Answer: 7

Question 5

Identify the mode of the dataset: 7, 3, 9, 4, 8.

Answer 5

No repeats
Answer: No mode

Question 6

From Page 31, calculate the mean for the marks: 10 (5 students), 12 (8 students), 14 (1 student), 16 (7 students), 20 (5 students).

Answer 6

Marks: 10 (5), 12 (8), 14 (1), 16 (7), 20 (5)
ΣfX = (10 × 5) + (12 × 8) + (14 × 1) + (16 × 7) + (20 × 5) = 50 + 96 + 14 + 112 + 100 = 372
Σf = 5 + 8 + 1 + 7 + 5 = 26
Mean = 372 / 26 ≈ 14.31
Answer: 14.31

Question 7

Find the median mark from the discrete data on Page 31.

Answer 7

Cumulative freq.: 5 (10), 13 (12), 14 (14), 21 (16), 26 (20)
Median position = 13.5 (between 13th and 14th)
13th = 12, 14th = 14 → Median ≈ 13
Answer: 13 (approx.)

Question 8

Determine the modal mark from Page 31.

Answer 8

Highest frequency: 8 (12)
Answer: 12

Question 9

For a dataset with marks: 5 (3 students), 10 (4 students), 15 (5 students), calculate the mean.

Answer 9

Marks: 5 (3), 10 (4), 15 (5)
ΣfX = (5 × 3) + (10 × 4) + (15 × 5) = 15 + 40 + 75 = 130
Σf = 3 + 4 + 5 = 12
Mean = 130 / 12 ≈ 10.83

Question 10

From Page 25, calculate the mean delivery time (midpoint method) for: 10-20 (3), 20-30 (5), 30-40 (9), 40-50 (7), 50-60 (6).

Answer 10

Midpoints: 15, 25, 35, 45, 55
ΣfX = (15 × 3) + (25 × 5) + (35 × 9) + (45 × 7) + (55 × 6) = 45 + 125 + 315 + 315 + 330 = 1130
Σf = 30
Mean = 1130 / 30 ≈ 37.67

Question 11

Find the median delivery time range from Page 25.

Answer 11

Cumulative freq.: 3, 8, 17, 24, 30
Median position = 15.5 (between 15th and 16th), in 30-40 range
Answer: 30-40 minutes

Question 12

Identify the modal delivery time range from Page 25.

Answer 12

Highest frequency: 9 (30-40)
Answer: 30-40 minutes

Question 13

From Page 32, calculate the mean salary (in ‘000 Rands) for: 10-15 (5), 15-20 (8), 20-25 (12), 25-30 (7), 30-35 (4).

Answer 13

Midpoints: 12.5, 17.5, 22.5, 27.5, 32.5
ΣfX = (12.5 × 5) + (17.5 × 8) + (22.5 × 12) + (27.5 × 7) + (32.5 × 4) = 62.5 + 140 + 270 + 192.5 + 130 = 795
Σf = 36
Mean = 795 / 36 ≈ 22.08

Question 14

Determine the median salary range from Page 32.

Answer 14

Cumulative freq.: 5, 13, 25, 32, 36
Median position = 18 (in 20-25 range)
Answer: 20-25 (‘000 Rands)

Question 15

Find the modal salary range from Page 32.

Answer 15

Highest frequency: 12 (20-25)
Answer: 20-25 (‘000 Rands)

Question 16

For a dataset: 2, 4, 4, 6, 8, calculate the mean.

Answer 16

Data: 2, 4, 4, 6, 8
Sum = 24, Mean = 24 / 5 = 4.8
Answer: 4.8

Question 17

Find the median of: 2, 4, 4, 6, 8.

Answer 17

Ordered: 2, 4, 4, 6, 8
Median = 4
Answer: 4

Question 18

From Page 34, calculate the mean of the first 5 scores: 50, 53, 59, 59, 63.

Answer 18

Data: 50, 53, 59, 59, 63
Sum = 284, Mean = 284 / 5 = 56.8
Answer: 56.8

Question 19

Determine the mode of the first 10 scores on Page 34: 50, 53, 59, 59, 63, 63, 72, 72, 72, 72.

Answer 19

Data: 50, 53, 59, 59, 63, 63, 72, 72, 72, 72
Most frequent: 72 (4 times)
Answer: 72