Question

The following weights are for 16 Grizzly Bears in North America. They are:  

125, 114, 108, 135, 144, 124, 110, 152, 134, 117, 98, 116, 202, 225, 169, 160

1. Find the Mean, Median, Range and Population Standard Deviation to the nearest tenth.
2. Find the Z-Score of the female bear that weighs 134kg
3. Make a box and whisker plot.
4. Determine if there are any outliers in your plot. FIND IQR.
5. Determine the shape of the distribution.

Answer 1

	X	x-	(x-)2
1	98	-41.5625	1727.441
2	108	-31.5625	996.1914
3	110	-29.5625	873.9414
4	114	-25.5625	653.4414
5	116	-23.5625	555.1914
6	117	-22.5625	509.0664
7	124	-15.5625	242.1914
8	125	-14.5625	212.0664
9	134	-5.5625	30.94141
10	135	-4.5625	20.81641
11	144	4.4375	19.69141
12	152	12.4375	154.6914
13	160	20.4375	417.6914
14	169	29.4375	866.5664
15	202	62.4375	3898.441
16	225	85.4375	7299.566
Total	2233	0	18477.94

Find the Mean, Median, Range and Population Standard Deviation to the nearest tenth.

Mean	139.5625
Median (2nd quartile)	129.5
Range  (Max - Min)	127
Pop SD	33.983

Find the Z-Score of the female bear that weighs 134kg

z-score = ​​​​​​​

x = 134

z-score = -0.1637

Make a box and whisker plot.

For the five point summary we need min,Q1,Q2,Q3,max. Where the quartiles use the following formula

	th value	value
Q1	4.25	114.5
Q2	8.5	129.5
Q3	12.75	158

Summary

Min	98
Q1	114.5
Q2	129.5
Q3	158
Max	225

Determine if there are any outliers in your plot. FIND IQR.

To check for outlier we see if any value falls outside the range (Q1-1.5IQR, Q3 - 1.5IQR) where IQR = Q3-Q1

IQR = 43.5

range = (49.25, 223.25)

Outliers : 225

Determine the shape of the distribution.

Since the median line is to the left and there is space towards the right also Mean > Median, so it right or positively skewed.