Question

math test scores
stems leaves
6 5 8
7 0 1 1 4 7
8 5 5 7 8 9 9 9
9 2 4 5 8 8
10 0 0
find the following data landmarks for the math test scores by using the stem - and - leaf plot.
maximum
minimum
range
mode
median
mean
pieces of candy
stems leaves
0 8 9
1 2 5 5 5 7
2 3 3 4 7 8 8 8 8 9
3 0 0 1 1 6
4 1
find the following data landmarks for the pieces of candy by using the stem - and - leaf plot.
maximum
minimum
range
mode
median
mean

Explanation:

Step1: Identify maximum for math test scores

The largest number in the stem - and - leaf plot is 100.

Step2: Identify minimum for math test scores

The smallest number is 65.

Step3: Calculate range for math test scores

Range = Maximum - Minimum = 100 - 65 = 35.

Step4: Identify mode for math test scores

The number 89 and 98 both appear twice, so the modes are 89 and 98.

Step5: Calculate median for math test scores

There are 20 data points. The median is the average of the 10th and 11th ordered data points. The 10th value is 87 and the 11th value is 89. Median=$\frac{87 + 89}{2}=88$.

Step6: Calculate mean for math test scores

Sum of all scores:
\[

$$\begin{align*} &65+68 + 70+71+71+74+77+85+85+87+88+89+89+89+92+94+95+98+98+100\\ =&1730 \end{align*}$$

\]
Mean=$\frac{1730}{20}=86.5$.

Step7: Identify maximum for pieces of candy

The largest number is 41.

Step8: Identify minimum for pieces of candy

The smallest number is 8.

Step9: Calculate range for pieces of candy

Range = 41 - 8 = 33.

Step10: Identify mode for pieces of candy

The number 28 appears 4 times, so the mode is 28.

Step11: Calculate median for pieces of candy

There are 20 data points. The median is the average of the 10th and 11th ordered data points. The 10th value is 24 and the 11th value is 27. Median=$\frac{24 + 27}{2}=25.5$.

Step12: Calculate mean for pieces of candy

Sum of all values:
\[

$$\begin{align*} &8+9+12+15+15+15+17+23+23+24+27+28+28+28+28+29+30+30+31+31+36+41\\ =&438 \end{align*}$$

\]
Mean=$\frac{438}{22}\approx19.91$.

Answer:

Math Test Scores:
Maximum: 100
Minimum: 65
Range: 35
Mode: 89, 98
Median: 88
Mean: 86.5

Pieces of Candy:
Maximum: 41
Minimum: 8
Range: 33
Mode: 28
Median: 25.5
Mean: 19.91