Mean median mode and midrange of grouped data
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Mean, Median, Mode, and Midrange of Grouped Data. Section 2.5. Grouped Data……. You must add one more column than you did using ungrouped data. You now need a midpoint column. The symbol for the midpoint is. Formulas……Mean. Mean. Median.

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Mean, Median, Mode, and Midrange of Grouped Data

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Mean median mode and midrange of grouped data

Mean, Median, Mode, and Midrange of Grouped Data

Section 2.5


Grouped data

Grouped Data……

  • You must add one more column than you did using ungrouped data.

  • You now need a midpoint column.

  • The symbol for the midpoint is .


Formulas mean

Formulas……Mean

  • Mean


Median

Median

  • There IS a formula to find the median using grouped data.


Mean median mode and midrange of grouped data

Mode……

  • Find the greatest frequency and read across the chart until you see the class that corresponds to it.

  • Your answer will be the entire interval.


Midrange

Midrange…..

  • Add the lowest number in the first row to the highest number in the last row.

  • Divide that answer by 2.


Example

Example…..

  • Find the mean, median, and mode of the set of grouped data.


Here is the list you should have

Here is the list you should have……


Mean median mode and midrange of grouped data

Mean……


Median1

Median…..

  • n/2 = 20/2 = 10


Plug values into formula

Plug values into formula….


Mode and midrange

Mode and Midrange……

  • The mode is 21-26.

  • Midrange =


Now you try

Now you try……….

  • Find the mean, median, and mode of the following set.


Your finished list

Your finished list…….


Mean median mode and midrange of grouped data

Mean……


Median2

Median…….


Mean median mode and midrange of grouped data

Mode……..

  • The mode is 69-72.


Midrange1

Midrange……..

  • The midrange =

    (63 + 78)/2 = 70.5


Range variance and st deviation grouped

Range, Variance and St. Deviation – Grouped

Section 2.5


Grouped data1

Grouped Data……

  • Variance Formula


Mean median mode and midrange of grouped data

  • Standard Deviation


Range

Range…..

  • High number in last row minus low number in first row.


Example1

Example……

  • Find the variance, standard deviation, and range of the set.


Calculator steps

Calculator Steps……

  • Put lower boundaries in L1 and upper boundaries in L2. Put frequencies in L3. Set a formula for midpoint in L4.


Mean median mode and midrange of grouped data

  • Find f times midpoint by setting a formula in L5.


Mean median mode and midrange of grouped data

  • Find f times midpoint squared in L6 by setting a formula.


Your lists should look like this

Your lists should look like this……


Mean median mode and midrange of grouped data

  • Find the variance.


Mean median mode and midrange of grouped data

  • Find the standard deviation.


Range high low

Range = High - Low

  • Range = 32 – 2 = 30


Example2

Example……

  • Find the mean, median, mode, midrange, range, variance, and st. deviation of the data set.


Here are the lists

Here are the lists……


Mean median mode and midrange of grouped data

Mean:


Median3

Median……


Mean median mode and midrange of grouped data

Mode……

  • Greatest Frequency is 9.

  • Mode = 15-20


Midrange2

Midrange……


Range1

Range……


Variance

Variance……


St deviation

St. Deviation……


Homework

Homework…….

  • Find the measures of center and variation for the grouped data on HW3.


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