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These line plots show the number of minutes two different age groups of teenagers spent online the previous week.

Two line plots, both are labeled from twelve to thirty six going by ones underneath the line plot. The top line represents Hours spent online parenthesis ages thirteen to fifteen parenthesis. There are three Xs over twenty eight, two Xs over twenty seven and one X over twenty one, twenty four, twenty six, thirty one and thirty four. The bottom line represents Minutes spent online parenthesis ages sixteen to eighteen years old parenthesis. There are four Xs over twenty eight and one X over twelve, twenty one, twenty seven, thirty point five, thirty four, thirty five and thirty six.

Select from the drop-down menus to complete each statement.

The range is
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. The mean
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1 answer

To calculate the range and the mean for each age group, we first need to summarize the data clearly.

Ages 13-15:

  • Data points: 21, 24, 26, 27, 28 (with frequencies: 1, 1, 1, 2, 3 respectively)
  • Total values:
    • 21 * 1 = 21
    • 24 * 1 = 24
    • 26 * 1 = 26
    • 27 * 2 = 54 (27 × 2 because there are 2 Xs)
    • 28 * 3 = 84 (28 × 3 because there are 3 Xs)

Sum of values:

  • \( 21 + 24 + 26 + 54 + 84 = 209 \)
  • Total number of entries: \( 1 + 1 + 1 + 2 + 3 = 8 \)

Mean (Ages 13-15):

  • Mean = Total Sum / Number of Entries = \( 209 / 8 = 26.125 \)

Range (Ages 13-15):

  • Max value = 28, Min value = 21, so Range = 28 - 21 = 7

Ages 16-18:

  • Data points: 12, 21, 27, 28, 30.5, 34, 35, 36 (with frequencies: 1, 1, 1, 4 respectively)
  • Total values:
    • 12 * 1 = 12
    • 21 * 1 = 21
    • 27 * 1 = 27
    • 28 * 4 = 112 (28 × 4 because there are 4 Xs)
    • 30.5 * 1 = 30.5
    • 34 * 1 = 34
    • 35 * 1 = 35
    • 36 * 1 = 36

Sum of values:

  • \( 12 + 21 + 27 + 112 + 30.5 + 34 + 35 + 36 = 277.5 \)
  • Total number of entries: \( 1 + 1 + 1 + 4 + 1 + 1 + 1 + 1 = 10 \)

Mean (Ages 16-18):

  • Mean = Total Sum / Number of Entries = \( 277.5 / 10 = 27.75 \)

Range (Ages 16-18):

  • Max value = 36, Min value = 12, so Range = 36 - 12 = 24

Complete the statements:

  • The range for ages 13-15 is 7 and for ages 16-18 is 24.
  • The mean for ages 13-15 is 26.125 and for ages 16-18 is 27.75.

Final statements for your drop-down:

  1. The range is 7 for ages 13-15 and 24 for ages 16-18.
  2. The mean is 26.125 for ages 13-15 and 27.75 for ages 16-18.