Question

1. given the following data: 164, 175, 126, 135, 159, 143, 55

a) what effect will the outlier have on the median of the data if the outlier is excluded?
b) what effect will the outlier have on the mean of the data if the outlier is excluded?
c) what effect will the outlier have on the mode of the data if the outlier is excluded?
d) what effect will the outlier have on the range of the data if the outlier is excluded?

Explanation:

Step1: Identify the outlier

The outlier is 55 as it is far - from the other values.

Step2: Arrange data in ascending order

Original data in ascending order: 55, 126, 135, 143, 159, 164, 175.

Step3: Calculate original median

There are 7 data points. Median is the 4th value, so original median $= 143$.

Step4: Calculate new median after excluding outlier

New data (excluding 55): 126, 135, 143, 159, 164, 175. There are 6 data points. Median is the average of the 3rd and 4th values, $\frac{143 + 159}{2}=151$. The median increases.

Step5: Calculate original mean

Original mean $\bar{x}_1=\frac{55 + 126+135 + 143+159+164+175}{7}=\frac{957}{7}\approx136.71$.

Step6: Calculate new mean after excluding outlier

New mean $\bar{x}_2=\frac{126 + 135+143+159+164+175}{6}=\frac{902}{6}\approx150.33$. The mean increases.

Step7: Analyze mode

Original data has no mode (no repeated values). After excluding 55, still no mode. So the mode is unaffected.

Step8: Calculate original range

Original range = 175 - 55 = 120.

Step9: Calculate new range after excluding outlier

New range = 175 - 126 = 49. The range decreases.

Answer:

a) The median increases.
b) The mean increases.
c) The mode is unaffected.
d) The range decreases.