Use the grouped data formulas to find the indicated mean or standard deviation.
-The speeds of a random sample of 100 cars are recorded as they pass a highway checkpoint. The results are summarized in the frequency distribution below. Approximate the sample mean. $$\begin{array} { r | r }
\text { Speed (mph) } & \text { Cars } \
\hline 30 - 39 & 3 \
40 - 49 & 17 \
50 - 59 & 50 \
60 - 69 & 19 \
70 - 79 & 11
\end{array}$$
A)56.3 mph
B)54.5 mph
C)61.9 mph
D)59.1 mph

Question

Use the grouped data formulas to find the indicated mean or standard deviation.
-The speeds of a random sample of 100 cars are recorded as they pass a highway checkpoint. The results are summarized in the frequency distribution below. Approximate the sample mean. $$\begin{array} { r | r } 
\text { Speed (mph) } & \text { Cars } \
\hline 30 - 39 & 3 \
40 - 49 & 17 \
50 - 59 & 50 \
60 - 69 & 19 \
70 - 79 & 11
\end{array}$$
A)56.3 mph
B)54.5 mph
C)61.9 mph
D)59.1 mph

Quizplus · Accepted Answer

To approximate the sample mean for grouped data, we use the formula: $\bar{x} = \frac{\sum{f \cdot x}}{N}$, where $f$ is the frequency of each group, $x$ is the midpoint of each group, and $N$ is the total number of observations. 1. Calculate the midpoint of each speed interval:    - $30 - 39: 34.5$   - $40 - 49: 44.5$   - $50 - 59: 54.5$   - $60 - 69: 64.5$   - $70 - 79: 74.5$2. Multiply each midpoint by its frequency:   - $3 \times 34.5 = 103.5$   - $17 \times 44.5 = 756.5$   - $50 \times 54.5 = 2725$   - $19 \times 64.5 = 1225.5$   - $11 \times 74.5 = 819.5$3. Sum these products and divide by the total number of cars (100):   - $\frac{103.5 + 756.5 + 2725 + 1225.5 + 819.5}{100} = \frac{5630}{100} = 56.3$ mph.Therefore, the approximate sample mean speed is 56.3 mph.

Use the Grouped Data Formulas to Find the Indicated Mean