Question 1085685: An experimental station recorded the following data:
32 29 34 31 35 35 27 32 38 37 31 38
36 35 31 36 39 41 38 31 33 41 28 30
39 39 31 37 36 32 30 39 35 32 33 38
34 42 33 33 41 30 31 34 30 33 29 32
49 30 34 33 35 33 33 35 29 35 35 42
32 35 28 36 31 32 39 26 33 34 36 32
i. Make a frequency table using five classes
ii. Draw a histogram from the table in (i) above
iii. Calculate the median, the mean and the Standard Deviation of the data set.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Note: It's not clear what the data values in the table represent, so I'm going to be a bit vague with the frequency table and histogram labels for the x values. I'll refer to them as "class interval".
------------------------------------------------------------------------------------------------
Part i)
The smallest value is 26. The largest value is 49. If we start at 25, and have each class interval of width 5 units, then we'll be able to create 5 classes like so:
25-29, 30-34, 35-39, 40-44, 45-49
Now what you do next is look through the data and for each data value, determine which class it belongs to. For example, the value 32 belongs in the second class labeled "30-34". You'll add one to the frequency for this class interval. You repeat these steps for every other data value.
This can get tedious because there are 72 data values (6 rows, 12 columns). So it's best to use software to help count and sort the data properly. That way no human error is made.
After doing all the sorting and counting of the values, you should have the following grouped frequency table
I used Microsoft Excel to generate the table. Free alternatives like OpenOffice will be able to do the same.
------------------------------------------------------------------------------------------------
Part ii)
To construct a histogram, refer to the grouped frequency table from part i). There will be 5 bars. Each bar's height corresponds exactly to the frequency value. For example, the bar for the class interval "25-29" is 7 units high because this is the frequency paired with this class interval. The other bars are drawn in a similar fashion. You should get this histogram
I used Microsoft Excel to generate the histogram. Free alternatives like OpenOffice will be able to do the same.
------------------------------------------------------------------------------------------------
Part iii)
To find the median, sort the values from smallest to largest. Then pick out the middle most value. In this case, there are an even number of values (n = 72) so the middle is actually between two values. The two middle most values are 33 and 34. The middle of which is 33.5 since (33+34)/2 = 33.5. The value 33.5 is the midpoint of 33 and 34.
To find the mean, add up all the data values and divide the sum by 72
If we add up all the data values, we get the sum 2458. You can type each value into the calculator, or use excel's SUM function.
Now divide 2458 by 72 to get 2458/72 = 34.13889 which is approximate
Therefore, the mean is roughly 34.13889
Because there are so many values, I'll simply skip to using the STDEV function in excel. It is the sample standard deviation for a set of values. In this case, excel spits out 4.074328962 which is approximate.
If you wish to find the population standard deviation, then use the STDEVP function in excel to get roughly 4.04593608
It's not entirely clear which standard deviation your teacher wants, so I'm writing both of them.
I have a feeling the population version is what your teacher wants, but I'm not 100% sure on that.
Summary:
Median = 33.5
Mean = 34.13889
Sample Standard Deviation = 4.074328962
Population Standard Deviation = 4.04593608
|
|
|
