Short & Long Answer Questions: Connecting the Dots....

Q1. Why does removing an outlier often increase the mean in a dataset?

Ans: If the outlier is too low, it pulls the mean down.
Removing it:

• raises total sum per value
• increases average naturally

Example:
2, 3, 4, 5, 50
Mean is high due to 50.

But if outlier = 0, removing it increases the mean.

Thus, mean changes strongly depending on the outlier's position.

Q2.  The heights (in cm) of 9 girls in a class are:

139, 142, 145, 150, 152, 138, 147, 140, 190

(a) Find the mean and median.
(b) Identify the outlier and recalculate mean without it.
(c) Explain whether mean or median represents the group better.

Ans: Step 1: Mean (with outlier)

Sum = 139 + 142 + 145 + 150 + 152 + 138 + 147 + 140 + 190 = 1343
Mean = 1343 ÷ 9 ≈ 149.22 cm

Step 2: Median

Sorted:
138, 139, 140, 142, 145, 147, 150, 152, 190
Median = 145 cm

Step 3: Identify Outlier

190 is extremely high compared to others (138-152).

Remove 190.

New sum = 1343 - 190 = 1153
New count = 8
New mean = 1153 ÷ 8 ≈ 144.1 cm

Step 4: Compare

• Mean changed from 149.22 → 144.1 (big change)
• Median stayed close to actual central value (145 cm)

Conclusion:

Median is better because it is stable even when outliers exist. Mean gets distorted by the unusually tall height of 190 cm.

Q3. The number of pages read by two students in a week is as follows:

Student A: 10, 12, 9, 11, 8, 7, 13
Student B: 5, 24, 6, 4, 7, 25, 5

(a) Find mean and median for both students.
(b) Who shows more consistent reading habits? Explain using spread.
(c) Who appears to be a better reader overall? Justify.

Ans: Student A's Mean

Sum = 10 + 12 + 9 + 11 + 8 + 7 + 13 = 70
Mean = 70 ÷ 7 = 10 pages

Student A's Median

​Sorted: 7, 8, 9, 10, 11, 12, 13
Median = 10 pages

Student B's Mean

Sum = 5 + 24 + 6 + 4 + 7 + 25 + 5 = 76
Mean = 76 ÷ 7 ≈ 10.86 pages

Student B's Median

​Sorted: 4, 5, 5, 6, 7, 24, 25
Median = 6 pages

Conclusion:
Student A range: 7 to 13 → 6 pages spread (very stable)
Student B range: 4 to 25 → 21 pages spread (highly unstable)

Student A is more consistent.

Q5. A cricket team played 5 matches and scored:
84, 13, 0, 57, 51

(a) Calculate the mean runs per match.
(b) Find the median.
(c) Explain how the "0" run affects the mean but not the median.
(d) Which measure better represents player performance?

Ans: (a) Mean

​Sum = 84 + 13 + 0 + 57 + 51 = 205
Mean = 205 ÷ 5 = 41 runs

(b) Median

​Sorted: 0, 13, 51, 57, 84
Median = 51 runs

(c) 

• Zero drags the mean down to 41 even though three scores are 51 or higher.
• Median remains 51 because it depends only on the middle value.

(d) Median is better because most performances were above 51.

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