Question

In: Statistics and Probability

A farmer records the number of bees spotted on his farm over a two week period...

A farmer records the number of bees spotted on his farm over a two week period in the middle of the summer. Below is a stem and leaf plot of his data:

1 67
2 269
3 29
4 399
5 4
6 14
7
8 7

key: 1 6=16

1) Find the mean, median, mode, and sample standard deviation for this data

2) List the values for your Five Number Summary for the data in order.

3) Identify any outliers using the IQR Method

4) ) If the true distribution for number of bees on the farm on a given day at this time of year is normal with a mean of 45 and a standard deviation of 15, find the z-score for a day when 32 bees are observed. Is this an unusual number of bees to see during the day at this time of year?

Solutions

Expert Solution

1.

Mean

42

Median

41

Mode

49

stdev

20.283

2.

Five number summary

minimum

16

Q1

26.75

Q2

41

Q3

52.75

Maximum

87

3.

IQR (Q3-Q1)

26

Q1-1.5*IQR

-12.25

Q3+1.5IQR

91.75

No number is < -12.25 and no number is > 91.75. Hence there are no outliers

# bees
16
17 QNo
22 Q2 Five number summary
26 minimum 16
29 Q1 26.75
32 Q2 41
39 Q3 52.75
43 Maximum 87
49
49
54 Q3 IQR (Q3-Q1) 26
61 Q1-1.5*IQR -12.25
64 Q3+1.5IQR 91.75
87
Q1 Mean 42 Q4 Z score -0.867
Median 41
Mode 49
stdev 20.283

Excle function used

orchestra answered 2 years ago
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