3. Sixteen milk-yielding Ayrshire cows were fed a diet of silage that was supple

ID: 3040167 • Letter: 3

Question

3. Sixteen milk-yielding Ayrshire cows were fed a diet of silage that was supplemented with a vitamin con- tentrate. The following values refer to the milk fat concentration (g/kg) for each cow 20, 38, 44, 49, 42, 21, 48, 47 21, 22, 23, 26, 26, 44, 48, 29 (a) Create a stem-and-leaf display with two lines per stem. (b) What interesting feature of the data is made apparent when put into the stem-and-leaf display? (c) Calculate the mean averagel and median and explain why reporting a center for this data (mean or median) without providing a graph of the data is not very useful. 4. The back-to-back split stemplot shows the lifetimes of 15 Brand X and Brand Y batteries (number down the middle gives the stem and numbers under Brand X and Brand Y are leaves). Brand 21103 997753 3221 4 223334 456889 Key: 2141 or 2 represents 420429 bours for Brand X and Brand Y, respectively (a) What is the longest that any battery lasted? (b) Give a reason someone might prefer a Brand X battery (c) Give a reason someone might prefer a Brand Y battery

Explanation / Answer

Result:

3).

a).

Stem and Leaf plot for

Fat

stem unit =

leaf unit =

Frequency

Stem

Leaf

0 1 1 2 3

6 6 9

2 4 4

7 8 8 9

b).

The distribution is U shaped. Frequency of low and high values are more compared to middle values.

c).

Descriptive statistics

Fat

mean

34.25

sample standard deviation

11.60

minimum

maximum

1st quartile

22.75

median

33.50

Mean is 34.25 and median is 33.50.

Median is appropriate for this data because data are skewed.

4).

a). largest value is 55 ( Brand X)

b).

Most of the values are clustered in middle and there is less variability in the data.

Someone think it is reliable.

c).

Frequencies are high large values and expect a large life time.