How do you SOlve? what are the steps

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steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Sorry, nhl.  I copied part of a MS Excel spreadsheet I used into the answer.  The system didn't take it apparently.  Trying to tell you how to read it, the lowest value, 145, was the first value, #1.  So, we have the "145 1".  The 4th value was 157.  So, we have "157 4".

Sorry, nhl.  I hope this helps.

Till Then,

Steve

steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Hi, nhl.  I hope I can assist with this.

First, we need to put the numbers in order, preferably from lowest to highest.  So, we have:

145 1 151 2 154 3 157 4 158 5 160 6 162 7 162 8 164 9 165 10 166 11 168 12 169 13 171 14 171 15 173 16 175 17 175 18 177 19 179 20 180 21 182 22 183 23 186 24 188 25

Notice, to the right of the values, I put the value number next to the number.  For instance, the first value, n1 = 145The 4th value, n4 = 157.  And, so forth.

Now, from these, to find the value for a certain percentile, we can use:

Pk = (n+1)k/100

Where k is the percentile value.  For instance, if we are looking for the median, the 50th percentile, k = 50, so the median would be P50.  And, plugging in the values:

P50 = (25+1)50/100 = 13

Which tells us the 13th value would be the 50th percentile, which is 169.

We first find where the percentile would be in the order.  Then, we find what the specific value would be.



For, for where P70 is:

P70 = (25+1)70/100 = 18.2

Now, here, we are between the 18th and 19th value.  There are several ways here to work.  I normally take the average of the two values in question.  So:

(175+177)/2 = 176 would be P70.

For D6, that's the same as P60.  So, we plug in 60 into the formula:

P60 = (25+1)60/100 = 15.6

That makes it between the 15th and 16th values.  So:

P60 = (171+173)/2 = 172

For Q3, that's the same as finding P75.  So:

P75 = (25+1)75/100 = 19.5, between the 19th and 20th values

P75 = (177+179)/2 = 178 = Q3

For the interquartile range, that's P75 - P25.  We have P75.  So, now, we need P25.  For that:

P25 = (25+1)25/100 = 6.5, between the 6th and 7th values

P25 = (160 + 162)/2 = 161

Then, interquartile range = Q3 - Q1 = P75 - P25 =

178 - 161 = 17

For the semi-interquartile range, we would divide the interquartile range by 2.  So:

semi-interquartile range = 17/2 = 8.5

For the mid-quartile range, we would add Q3 and Q1, which were P75 and P25, then divide them by 2.  So:

midquartile range = (178+161)/2 = 169.5

For the 10-90 percentile range, we would subtract P90 - P10.  So, we need to find P90 and P10.  For P90:

P90 = (25+1)90/100 = 23.4, so it is between the 23th and

                                                      24th values

P90 = (183+186)/2 = 184.5


For P10:

P10 = (25+1)10/100 = 2.6, so it is between the 2nd and

                                                      3rd values

P10 = (151+154)/2 = 152.5

Subtracting P90 - P10:

184.5 - 152.5 = 32 is the 10-90 percentile range.

Good luck, nhl.  I hope this helped.

Till Then,

Steve

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