Question

sixteen students each measured the weight of 25 pennies, in grams. the list shows their measurements.
60, 62, 65, 59, 63, 63, 63, 62, 64, 62, 60, 61, 66, 64, 61, 65
in each graph below, the mean is indicated by a solid vertical line segment while the standard deviations from the mean are indicated by dotted vertical line segments. which graph represents the distribution of weights?

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
Here, $n = 16$, and $\sum_{i=1}^{16}x_{i}=60 + 62+65 + 59+63+63+63+62+64+62+60+61+66+64+61+65$
$=60\times2+61\times2+62\times3+63\times3+64\times2+65\times2+59 + 66$
$=120+122+186+189+128+130+59+66$
$=1000$.
So, $\bar{x}=\frac{1000}{16}=62.5$.

Step2: Analyze the range of data

The data set is \(59,60,60,61,61,62,62,62,63,63,63,64,64,65,65,66\). The minimum value is \(59\) and the maximum value is \(66\).
The second graph has a range from \(52\) to \(74\) which is much larger than the actual data range. The first graph has a range that is more in line with the data values (from approximately \(58\) to \(66\)) and the mean of \(62.5\) (solid - line) is also consistent with the first graph's central position.

Answer:

The first graph.