12-1 Organizing Data Using Matrices

Quick Review

You can use matrices to organize data. To add or subtract matrices that are the same size, add or subtract the corresponding elements. To multiply a matrix by a scalar, multiply each element by the scalar.

Example

What is the difference?

  [ 3 2 − 1 5 2 − 2 ] − [ 2 4 4 − 3 1 0 ] = [ 3 − 2 2 − 4 − 1 − 4 5 − ( − 3 ) 2 − 1 − 2 − 0 ]   = [ 1 − 2 − 5 8 1 − 2 ] table with 2 rows and 2 columns , row1 column 1 , table with 2 rows and 1 column , row1 column 1 , , row2 column 1 , . matrix with 3 rows and 2 columns , row1 column 1 , 3 , column 2 2 , row2 column 1 , negative 1 , column 2 5 , row3 column 1 , 2 , column 2 negative 2 , end matrix . minus . matrix with 3 rows and 2 columns , row1 column 1 , 2 , column 2 4 , row2 column 1 , 4 , column 2 negative 3 , row3 column 1 , 1 , column 2 0 , end matrix , end table , column 2 equals . matrix with 3 rows and 2 columns , row1 column 1 , 3 minus 2 , column 2 2 minus 4 , row2 column 1 , negative 1 minus 4 , column 2 5 minus . open , negative 3 , close , row3 column 1 , 2 minus 1 , column 2 negative 2 minus 0 , end matrix , row2 column 1 , , column 2 equals . matrix with 3 rows and 2 columns , row1 column 1 , 1 , column 2 negative 2 , row2 column 1 , negative 5 , column 2 8 , row3 column 1 , 1 , column 2 negative 2 , end matrix , end table

Exercises

Find each sum, difference, or product.

5. [ − 5 1 0 8 ] − [ 7 − 6 − 4 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , negative 5 , column 2 1 , row2 column 1 , 0 , column 2 8 , end matrix . minus . matrix with 2 rows and 2 columns , row1 column 1 , 7 , column 2 negative 6 , row2 column 1 , negative 4 , column 2 2 , end matrix
6. [ 0.4 1.5 3.2 − 3 1.5 − 2.1 ] + [ 4 3 6.3 − 7.2 1.9 − 0.5 ] . matrix with 3 rows and 2 columns , row1 column 1 , 0.4 , column 2 1.5 , row2 column 1 , 3.2 , column 2 negative 3 , row3 column 1 , 1.5 , column 2 negative 2.1 , end matrix . plus . matrix with 3 rows and 2 columns , row1 column 1 , 4 , column 2 3 , row2 column 1 , 6.3 , column 2 negative 7.2 , row3 column 1 , 1.9 , column 2 negative 0.5 , end matrix
7. − 4.2 [ 3 1.1 3 − 2 − 1 2.9 ] negative 4.2 . matrix with 3 rows and 2 columns , row1 column 1 , 3 , column 2 1.1 , row2 column 1 , 3 , column 2 negative 2 , row3 column 1 , negative 1 , column 2 2.9 , end matrix

12-2 Frequency and Histograms

Quick Review

The frequency of an interval is the number of data values in that interval. A histogram is a graph that groups data into intervals and shows the frequency of values in each interval.

Example

Below are the prices of the television models sold at an electronics store. What is a histogram of the data?

$1399 $1349 $999 $2149 $149 $279 $449 $379 $1379 $799 $3199 $1099 $499 $899 $949 $1799 $1699 $3499

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Exercises

Use the data to make a histogram.

8. customers: 141 128 132 141 152 169 121 133 131 156 142 136 135 144 135 153
9. workout times (min): 41 29 46 39 37 44 33 51 42 30

Tell whether each histogram is uniform, symmetric, or skewed.

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