Question

forty families were surveyed and asked to record the number of hours per week their television was in use. the results are shown in this frequency table.
number of hours\tfrequency
0-9\t1
10-19\t6
20-29\t15
30-39\t12
40-49\t2
50-59\t4
which histogram is an accurate representation of the data?
a. image of histogram

Explanation:

To determine the accurate histogram, we analyze the frequency table:

Step 1: Understand the Data

The frequency table has intervals (0–9, 10–19, 20–29, 30–39, 40–49, 50–59) with frequencies: 1, 6, 15, 12, 2, 4.

Step 2: Analyze Histogram Requirements

A histogram for grouped data (intervals) must:

• Have equal-width bars (all intervals here are 10 hours, so bar widths are equal).
• The height of each bar matches the frequency of its interval.

Step 3: Evaluate Bar Heights

• 0–9: Frequency = 1 (shortest bar).
• 10–19: Frequency = 6 (taller than 0–9, shorter than 20–29).
• 20–29: Frequency = 15 (tallest bar).
• 30–39: Frequency = 12 (shorter than 20–29, taller than 10–19).
• 40–49: Frequency = 2 (shorter than 10–19).
• 50–59: Frequency = 4 (taller than 40–49, shorter than 10–19).

Step 4: Match to Histogram

The correct histogram will have bars with heights corresponding to these frequencies (e.g., tallest at 20–29, next at 30–39, then 10–19, 50–59, 40–49, and shortest at 0–9).

Since the options are not fully visible, but using the frequency data, the accurate histogram will have:

• Bar for 0–9: height 1.
• Bar for 10–19: height 6.
• Bar for 20–29: height 15 (tallest).
• Bar for 30–39: height 12.
• Bar for 40–49: height 2.
• Bar for 50–59: height 4.

(Note: If options are labeled, select the one with these bar heights. For example, if option “X” has bars matching these frequencies, that is the answer.)

If we assume the visible partial histogram (e.g., the one with the tallest bar at 20–29, next at 30–39, etc.) is the correct one, the answer would correspond to that option.

For example, if the options include a histogram with:

• 0–9: 1 unit tall,
• 10–19: 6 units,
• 20–29: 15 units (tallest),
• 30–39: 12 units,
• 40–49: 2 units,
• 50–59: 4 units,

that is the accurate representation.

Answer:

To determine the accurate histogram, we analyze the frequency table:

Step 1: Understand the Data

The frequency table has intervals (0–9, 10–19, 20–29, 30–39, 40–49, 50–59) with frequencies: 1, 6, 15, 12, 2, 4.

Step 2: Analyze Histogram Requirements

A histogram for grouped data (intervals) must:

• Have equal-width bars (all intervals here are 10 hours, so bar widths are equal).
• The height of each bar matches the frequency of its interval.

Step 3: Evaluate Bar Heights

• 0–9: Frequency = 1 (shortest bar).
• 10–19: Frequency = 6 (taller than 0–9, shorter than 20–29).
• 20–29: Frequency = 15 (tallest bar).
• 30–39: Frequency = 12 (shorter than 20–29, taller than 10–19).
• 40–49: Frequency = 2 (shorter than 10–19).
• 50–59: Frequency = 4 (taller than 40–49, shorter than 10–19).

Step 4: Match to Histogram

The correct histogram will have bars with heights corresponding to these frequencies (e.g., tallest at 20–29, next at 30–39, then 10–19, 50–59, 40–49, and shortest at 0–9).

Since the options are not fully visible, but using the frequency data, the accurate histogram will have:

• Bar for 0–9: height 1.
• Bar for 10–19: height 6.
• Bar for 20–29: height 15 (tallest).
• Bar for 30–39: height 12.
• Bar for 40–49: height 2.
• Bar for 50–59: height 4.

(Note: If options are labeled, select the one with these bar heights. For example, if option “X” has bars matching these frequencies, that is the answer.)

If we assume the visible partial histogram (e.g., the one with the tallest bar at 20–29, next at 30–39, etc.) is the correct one, the answer would correspond to that option.

For example, if the options include a histogram with:

• 0–9: 1 unit tall,
• 10–19: 6 units,
• 20–29: 15 units (tallest),
• 30–39: 12 units,
• 40–49: 2 units,
• 50–59: 4 units,

that is the accurate representation.