This portfolio has been modified...use these data points and follow these steps for full credit.
1) Use these 15 numbers as your data points
141, 330, 292, 198, 263, 224, 149, 121, 223, 125, 126, 48, 111, 327, 238
2) Find the:
Mean=
Median=
Mode=
Range=
MAD (mean absolute deviation)=
IQR(Interquartile range of box n whisker plot)=
3) Create a box n whiskers plot of the data
1) Mean= 194.2
2) Median= 223
Mode= There is no mode in this data set (no repeated values)
Range= 282 (calculated by subtracting the smallest value, 48, from the largest, 330)
MAD (mean absolute deviation)= 76.63
To calculate the MAD, we first find the mean of the data set:
(141+330+292+198+263+224+149+121+223+125+126+48+111+327+238)/15= 194.2
Next, we find the absolute difference between each data point and the mean:
|141-194.2|= 53.2
|330-194.2|= 135.8
|292-194.2|= 97.8
|198-194.2|= 3.8
|263-194.2|= 68.8
|224-194.2|= 29.8
|149-194.2|= 45.2
|121-194.2|= 73.2
|223-194.2|= 28.8
|125-194.2|= 69.2
|126-194.2|= 68.2
|48-194.2|= 146.2
|111-194.2|= 83.2
|327-194.2|= 132.8
|238-194.2|= 43.8
Then we find the mean of these absolute differences:
(53.2+135.8+97.8+3.8+68.8+29.8+45.2+73.2+28.8+69.2+68.2+146.2+83.2+132.8+43.8)/15= 76.63
Therefore, the MAD is 76.63.
IQR(Interquartile range of box n whisker plot)= 107.5
To find the IQR, we first need to find the first quartile (Q1) and third quartile (Q3) of the data set:
- Arrange the data set in order from smallest to largest:
48, 111, 121, 125, 126, 141, 149, 198, 223, 224, 238, 263, 292, 327, 330
- Find the median (which is the same as the second quartile, Q2):
Median = (223 + 224)/2 = 223.5
- Find Q1 and Q3 using the lower half and upper half of the data set:
Lower half: 48, 111, 121, 125, 126, 141, 149, 198
Upper half: 238, 263, 292, 327, 330
- Q1 is the median of the lower half:
Q1 = (125 + 126)/2 = 125.5
- Q3 is the median of the upper half:
Q3 = (292 + 327)/2 = 309.5
- IQR is the difference between Q3 and Q1:
IQR = 309.5 - 125.5 = 107.5
Therefore, the IQR is 107.5.
3) Box n whiskers plot:
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/___________________\
48 330
can you simplify this
Sure!
1) Mean: Add all the numbers together and divide by how many there are.
2) Median: Put the numbers in order from smallest to largest, and find the middle number. If there's an even number of numbers, find the average of the two middle numbers.
Mode: The number that appears most often in the list.
Range: Subtract the smallest number from the largest number.
MAD (mean absolute deviation): Find the mean of the absolute differences between each number and the mean.
IQR (Interquartile range): Find Q1 (the median of the lower half of the data) and Q3 (the median of the upper half of the data), and subtract Q1 from Q3.
Box n whiskers plot: Draw a number line and mark Q1, the median (Q2), and Q3. Draw a box and whiskers around those marks to represent the IQR and range. The individual data points can be shown as dots or x's.