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  • What is the multiple regression equation for salary using experience and gender?
    The equation is \(Y=29.17+4.17X_1+3.33X_2\), where X_1 is years of experience and X_2 is gender dummy variable (0=female, 1=male).
  • How to predict salary for a female employee with 10 years experience using the regression equation?
    Substitute X_1=10 and X_2=0 into the equation: \(Y=29.17+4.17(10)+3.33(0)=70.87\) (\$1000s).
  • How to predict salary for a male employee with 10 years experience using the regression equation?
    Substitute X_1=10 and X_2=1 into the equation: \(Y=29.17+4.17(10)+3.33(1)=74.2\) (\$1000s).
  • What does a census mean in data collection?
    A census collects data from every individual in the population.
  • What sampling technique is used when interviewing students leaving a cafeteria at lunchtime?
    This is convenience sampling, which may cause non-representative sample bias.
  • Which graph is most appropriate to visualize annual average rainfall over 100 years?
    A line graph is best to show trends over time for quantitative data.
  • How to construct a frequency distribution with lower class limit 45 and class width 10?
    Create classes like 45-54, 55-64, etc., and count data points in each class.
  • What type of distribution is shown by a histogram with frequencies 4, 7, 12, 8, 3?
    The distribution is skewed right because frequencies rise then fall with a longer tail on the right.
  • How to synthesize employee counts {HR:12, IT:20, Sales:8} into a bar graph?
    Create bars with heights proportional to counts: HR=12, IT=20, Sales=8.
  • What does it mean if two pie charts show different percentages for the same category?
    The category's representation varies between the two datasets.
  • What does a point at x=60 and y=20 on a frequency polygon represent?
    The class with midpoint 60 has a frequency of 20.
  • How many dots are stacked above the number 4 in the dot plot for data [1,2,2,4,4,4,5]?
    There are three dots stacked above 4.
  • What is the first step in constructing a stemplot?
    Organize the data in increasing order.
  • Why connect points with segments in a time series graph?
    To visualize trends in the data over time.
  • How to calculate the mean of resting heart rates: 72, 78, 85, 80, 76, 79, 77, 82, 81?
    Sum all values and divide by 9; mean is approximately 78.9 bpm.
  • How to interpret changes in weights over two years using mean and median?
    If both mean and median increase, weights in Year 2 are higher than Year 1.
  • When might the mode not represent the center of data well?
    If the mode occurs rarely or is far from mean and median, it may not represent central tendency.
  • How to calculate sample standard deviation for data 32, 36, 40, 44, 48?
    Use formula \(s=\sqrt{\frac{\sum x^2 - (\sum x)^2/n}{n-1}}\) to find s ≈ 7.32.
  • Is a laptop priced at \$870 unusual if mean is \$1,200 and SD is \$180?
    No, because \$870 is within 2 standard deviations below the mean.