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The age of everyone who attends a snooker club is recorded, and the frequency table is created. Find an estimated mean age for those people in the snooker club. You need to round this to the nearest whole number.

[tex]\[
\begin{tabular}{|c|c|}
\hline Age & Frequency \\
\hline $14-18$ & 9 \\
\hline $19-23$ & 3 \\
\hline $24-28$ & 2 \\
\hline $29-33$ & 1 \\
\hline $34-38$ & 5 \\
\hline
\end{tabular}
\][/tex]

A. 26

B. 24

C. 22

Sagot :

GinnyAnsweridn
To find the estimated mean age of attendees at the snooker club using the provided frequency table, we will follow these steps:

### Step 1: List the Age Intervals and Frequencies
Given age intervals and their corresponding frequencies are:

- [tex]\( 14-18 \)[/tex]: 9 people
- [tex]\( 19-23 \)[/tex]: 3 people
- [tex]\( 24-28 \)[/tex]: 2 people
- [tex]\( 29-33 \)[/tex]: 1 person
- [tex]\( 34-38 \)[/tex]: 5 people

### Step 2: Calculate the Mid-Point of Each Age Interval
To find the mid-point of each age interval, we use the formula:
[tex]\[ \text{Mid-point} = \frac{\text{Lower Bound} + \text{Upper Bound}}{2} \][/tex]

Thus, the mid-points for each interval are:
- For [tex]\( 14-18 \)[/tex]: [tex]\( \frac{14 + 18}{2} = 16 \)[/tex]
- For [tex]\( 19-23 \)[/tex]: [tex]\( \frac{19 + 23}{2} = 21 \)[/tex]
- For [tex]\( 24-28 \)[/tex]: [tex]\( \frac{24 + 28}{2} = 26 \)[/tex]
- For [tex]\( 29-33 \)[/tex]: [tex]\( \frac{29 + 33}{2} = 31 \)[/tex]
- For [tex]\( 34-38 \)[/tex]: [tex]\( \frac{34 + 38}{2} = 36 \)[/tex]

### Step 3: Multiply Each Mid-Point by the Corresponding Frequency
Next, we multiply the mid-point of each interval by the corresponding frequency:

- [tex]\( 16 \times 9 = 144 \)[/tex]
- [tex]\( 21 \times 3 = 63 \)[/tex]
- [tex]\( 26 \times 2 = 52 \)[/tex]
- [tex]\( 31 \times 1 = 31 \)[/tex]
- [tex]\( 36 \times 5 = 180 \)[/tex]

### Step 4: Sum Up the Products
Now, we sum up these products to find the total sum of mid-points times frequencies:
[tex]\[ 144 + 63 + 52 + 31 + 180 = 470 \][/tex]

### Step 5: Sum the Frequencies
Sum the total frequencies to find the total number of people:
[tex]\[ 9 + 3 + 2 + 1 + 5 = 20 \][/tex]

### Step 6: Calculate the Estimated Mean Age
The estimated mean age is calculated by dividing the total sum of the mid-points times frequencies by the total number of people:
[tex]\[ \text{Estimated Mean} = \frac{\text{Total Mid-Point Frequency}}{\text{Total Frequency}} = \frac{470}{20} = 23.5 \][/tex]

### Step 7: Round to the Nearest Whole Number
Finally, we round 23.5 to the nearest whole number, which gives us:
[tex]\[ \text{Estimated Mean Age} \approx 24 \][/tex]

Therefore, the estimated mean age of the people attending the snooker club, rounded to the nearest whole number, is [tex]\( \boxed{24} \)[/tex].
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