Answer to Question #270443 in Statistics and Probability for Light

Question

farmer examines a new variety of pea and he does a count of the number of peas in 33 pods. His results were as follows:

4, 5,

7, 9, 3, 1, 11, 5, 6, 6, 4, 4, 4, 12, 8, 2, 3, 3, 6, 7, 8, 4, 4, 3, 2, 5, 5, 5, 8, 7, 6, 5.

Find the five number summaries (i.e. Least score, Lower quartile,

Middle quartile, Upper quartile, and Largest score).

Draw a box plot to show the above data.

Find the inter – quartile range

Based on your result in (ii) state whether the data are skewed or symmetrical. (1 mark) Determine whether there are any outliers in the data

Answer 1

Least to Greatest Value:

1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 11, 12

Least score = 1

Largest score = 12

Middle quartile: $Q_2=5$

Lower quartile: $Q_1=4$

Upper quartile: $Q_3=7$

inter – quartile range: $IQR=Q_3-Q_1=7-4=3$

for box plot:

lower limit for outliers: $Q_1-1.5IQR=4-1.5\cdot3=-0.5$

upper limit for outliers: $Q_3+1.5IQR=7+1.5\cdot3=11.5$

from box plot we can see that data are skewed left side

outlier is 12 > 11.5 (upper limit for outliers)