The Income data fileatthebook’swebsitereportsannualincomevaluesintheU.S.,in thousands ofdollars.

(a) Usingsoftware,constructahistogram.Describeitsshape.

(b) Finddescriptivestatisticstosummarizethedata.Interpretthem.

(c) The kernel densityestimation methodfindsasmooth-curveapproximationfora histogram. Ateachvalue,ittakesintoaccounthowmanyobservationsarenearby and theirdistance,withmoreweightgiventhosecloser.Increasingthe bandwidth increases theinfluenceofobservationsfurtheraway.Plotasmooth-curveapproxi-
mation forthehistogramofincomevalues,usingthe density function in R. Sum-
marize theimpactofincreasingandofdecreasingthebandwidth(option bw in the density function) substantiallyfromthedefaultvalue.17

(d) Constructandinterpretside-by-sideboxplotsofincomebyrace(B = Black,H = Hispanic, W = White). Comparetheincomesusingnumericaldescriptivestatistics.