Question

4.4 homework
name:
show all your work on separate sheet of paper

1. joanna counted the number of songs she listened to each day for two weeks. find the mean, median,

mode, and range of this data.
15, 14, 15, 16, 12, 12, 8, 8, 5, 12, 22, 24, 15, 13
mean:____median:__mode:__range:____

1. jibri counted the number of pages he read each day for 10 days. find the mean, median, mode, and

range of this data.
23, 99, 8, 24, 15, 50, 66, 25, 15, 15
mean:____median:__mode:__range:____

1. sierra counted the number of pages she used in her notebook each week. find the mean, median,

mode, and range of this data.
75, 70, 95, 80, 60, 90, 70, 60, 85, 55, 60, 65, 65, 65, 70, 73
mean:____median:__mode:__range:____

1. suppose that jerrel has test scores of 98, 95, 88, 94, 100, and 93. he has one test remaining and his

goal is to have a test average of exactly 95. what must jerrels score on his final test in order to meet his
goal?

1. sadé has test scores of 80, 99, 94, and 93. she took one more test and her average on all 5 tests was
2. what did sadé score on her last test?

Explanation:

Step1: Sort the data

Sort the data in ascending order.
For the first data set: \(5,8,8,12,12,12,13,14,15,15,15,16,22,24\)
For the second data set: \(8,15,15,15,23,24,25,50,66,99\)
For the third data set: \(55,60,60,60,65,65,65,70,70,70,73,75,80,85,90,95\)

Step2: Calculate the mean

The mean is the sum of all data values divided by the number of data values.

• First data set: \(\frac{5 + 8+8+12+12+12+13+14+15+15+15+16+22+24}{14}=\frac{191}{14}\approx13.64\)
• Second data set: \(\frac{8 + 15+15+15+23+24+25+50+66+99}{10}=\frac{330}{10} = 33\)
• Third data set: \(\frac{55+60+60+60+65+65+65+70+70+70+73+75+80+85+90+95}{16}=\frac{1128}{16}=70.5\)

Step3: Calculate the median

If the number of data values \(n\) is even, the median is \(\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\); if \(n\) is odd, the median is \(x_{\frac{n + 1}{2}}\) (where \(x_i\) is the \(i\) - th ordered data value)

• First data set (\(n = 14\)): \(\frac{13+14}{2}=13.5\)
• Second data set (\(n = 10\)): \(\frac{23+24}{2}=23.5\)
• Third data set (\(n = 16\)): \(\frac{70+70}{2}=70\)

Step4: Calculate the mode

The mode is the data value that appears most frequently.

• First data set: \(12\) and \(15\) (both appear \(3\) times)
• Second data set: \(15\) (appears \(3\) times)
• Third data set: \(60\) and \(65\) and \(70\) (all appear \(3\) times)

Step5: Calculate the range

The range is the difference between the maximum and minimum data values.

• First data set: \(24-5 = 19\)
• Second data set: \(99 - 8=91\)
• Third data set: \(95-55 = 40\)

Step6: Solve for the missing test score (Problem 4)

Let the score of the final test be \(x\). The mean formula \(\frac{98+95+88+94+100+93+x}{7}=95\)

$$98+95+88+94+100+93+x=95\times7$$

$$568+x = 665$$

$$x=665 - 568=97$$

Step7: Solve for the missing test score (Problem 5)

Let the score of the last test be \(y\). The mean formula \(\frac{80+99+94+93+y}{5}=93\)

$$80+99+94+93+y=93\times5$$

$$366+y=465$$

$$y = 465-366 = 99$$

Answer:

1. Mean: \(\approx13.64\), Median: \(13.5\), Mode: \(12\) and \(15\), Range: \(19\)
2. Mean: \(33\), Median: \(23.5\), Mode: \(15\), Range: \(91\)
3. Mean: \(70.5\), Median: \(70\), Mode: \(60\), \(65\) and \(70\), Range: \(40\)
4. \(97\)
5. \(99\)